Пример. Матричные функции нормы и определителя

Функции > Векторы и матрицы > Характеристики массива > Пример. Матричные функции нормы и определителя

Пример. Матричные функции нормы и определителя

1. Определите квадратную матрицу.

2. Задайте для элементов матрицы имена базовых переменных.

Щелкните для копирования этого выражения

<region id="ID0EKIEFB" actualWidth="111.93333333333334" actualHeight="69.37360000000001" top="230.40000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="44">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <matrix rows="3" cols="3">
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
        </id>
        <id labels="VARIABLE" xml:space="preserve">
          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
        </id>
      </matrix>
      <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

3. Используйте функцию norm1, чтобы найти норму L1 матрицы M.

Либо найдите норму L1, вычислив максимум абсолютных сумм столбцов матрицы M.

<region id="ID0ERLEFB" actualWidth="156.98000000000002" actualHeight="27.791200000000003" top="403.20000000000005" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="48">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
  </math>
</region>

<region id="ID0E6LEFB" actualWidth="156.98000000000002" actualHeight="27.791200000000003" top="441.60000000000008" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="50">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
  </math>
</region>

<region id="ID0ENMEFB" actualWidth="156.98000000000002" actualHeight="27.791200000000003" top="480.00000000000006" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="52">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
  </math>
</region>

<region id="ID0E2MEFB" actualWidth="261.61666666666667" actualHeight="27.791200000000003" top="518.40000000000009" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="54">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">N<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">L1</Subscript></Span>
      </id>
      <eval>
        <apply>
          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">max</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ACS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

4. Используйте функцию norm2, чтобы найти норму L2 матрицы M.

Либо используйте функцию svds, чтобы найти самое большое абсолютное сингулярное значение матрицы M.

Функция svds возвращает вектор сортированных сингулярных значений; таким образом, верхнее значение является самым большим сингулярным значением матрицы M.

5. Используйте функцию norme, чтобы найти евклидову норму матрицы M.

Или же вручную вычислите квадратный корень суммы абсолютных квадратов матрицы M.

<region id="ID0EHTEFB" actualWidth="509.50600031296426" actualHeight="36.780453040075308" top="940.80000000000018" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="62">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">N<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">e</Subscript></Span>
      </id>
      <eval>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <apply>
              <plus />
              <apply>
                <plus />
                <apply>
                  <plus />
                  <apply>
                    <plus />
                    <apply>
                      <plus />
                      <apply>
                        <plus />
                        <apply>
                          <plus />
                          <apply>
                            <pow />
                            <apply>
                              <absval />
                              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                              </id>
                            </apply>
                            <real>2</real>
                          </apply>
                          <apply>
                            <pow />
                            <apply>
                              <absval />
                              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                              </id>
                            </apply>
                            <real>2</real>
                          </apply>
                        </apply>
                        <apply>
                          <pow />
                          <apply>
                            <absval />
                            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                            </id>
                          </apply>
                          <real>2</real>
                        </apply>
                      </apply>
                      <apply>
                        <pow />
                        <apply>
                          <absval />
                          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                          </id>
                        </apply>
                        <real>2</real>
                      </apply>
                    </apply>
                    <apply>
                      <pow />
                      <apply>
                        <absval />
                        <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                          <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                        </id>
                      </apply>
                      <real>2</real>
                    </apply>
                  </apply>
                  <apply>
                    <pow />
                    <apply>
                      <absval />
                      <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                      </id>
                    </apply>
                    <real>2</real>
                  </apply>
                </apply>
                <apply>
                  <pow />
                  <apply>
                    <absval />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                  </apply>
                  <real>2</real>
                </apply>
              </apply>
              <apply>
                <pow />
                <apply>
                  <absval />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                </apply>
                <real>2</real>
              </apply>
            </apply>
            <apply>
              <pow />
              <apply>
                <absval />
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                  <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                </id>
              </apply>
              <real>2</real>
            </apply>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

6. Используйте функцию normi, чтобы найти бесконечную норму матрицы M.

Либо используйте функцию максимума, чтобы вручную вычислить максимум абсолютных сумм строк матрицы M.

<region id="ID0E6VEFB" actualWidth="158.77333333333334" actualHeight="27.791200000000003" top="1132.8000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="66">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0ENWEFB" actualWidth="156.48333333333335" actualHeight="27.791200000000003" top="1171.2000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="68">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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  <math resultRef="70">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
      </id>
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
          <apply>
            <absval />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply>
          <absval />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EJXEFB" actualWidth="252.23666666666671" actualHeight="27.791200000000003" top="1248.0000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="72">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">
        <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">N<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">i</Subscript></Span>
      </id>
      <eval>
        <apply>
          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">max</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

7. Используйте функцию det, чтобы найти определитель матрицы M.

Либо вручную вычислите определитель матрицы M.

<region id="ID0EB1EFB" actualWidth="490.83" actualHeight="27.791200000000003" top="1401.6000000000001" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="76">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">DET</id>
      <eval>
        <apply>
          <plus />
          <apply>
            <minus />
            <apply>
              <mult />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
              </id>
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                  </apply>
                  <apply>
                    <mult />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                    </id>
                  </apply>
                </apply>
              </parens>
            </apply>
            <apply>
              <mult />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
              </id>
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                  </apply>
                  <apply>
                    <mult />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                      <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                  </apply>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply>
            <mult />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
              <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
            <parens>
              <apply>
                <minus />
                <apply>
                  <mult />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                  </id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                </apply>
                <apply>
                  <mult />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                  </id>
                </apply>
              </apply>
            </parens>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

8. Используйте функцию norm, чтобы найти норму вектора, содержащего элементы столбца 0 матрицы M.

Щелкните для копирования этого выражения

<region id="ID0EH3EFB" actualWidth="109.26666666666668" actualHeight="69.37360000000001" top="1497.6000000000001" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="78">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">v</id>
      <eval>
        <matrix rows="3" cols="1">
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
            <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
        </matrix>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
  </math>
</region>

Либо вручную вычислите норму вектора v.

<region id="ID0EM4EFB" actualWidth="207.04933364629747" actualHeight="36.780453040075308" top="1632.0000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="82">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">N</id>
      <eval>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <apply>
              <plus />
              <apply>
                <pow />
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                  <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                </id>
                <real>2</real>
              </apply>
              <apply>
                <pow />
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                  <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                </id>
                <real>2</real>
              </apply>
            </apply>
            <apply>
              <pow />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
              </id>
              <real>2</real>
            </apply>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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