向量、矩陣及表格
>
使用陣列
> 範例：矩陣代數
範例：矩陣代數
1.
定義並轉置矩陣。
<region id="ID0EKUVGB" actualWidth="94.733333333333334" actualHeight="62.800000000000004" top="115.20000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="15"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">M</id> <matrix rows="3" cols="3"> <real>0</real> <real>3</real> <real>5</real> <real>1</real> <real>0</real> <real>3</real> <real>2</real> <real>2</real> <real>1</real> </matrix> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EYUVGB" actualWidth="110.98" actualHeight="62.800000000000004" top="192.00000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="16"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <transpose /> <id xml:space="preserve">M</id> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
2.
計算矩陣的行列式。
<region id="ID0EIWVGB" actualWidth="77.733333333333334" actualHeight="25.6" top="288.00000000000006" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="17"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <determinant /> <id xml:space="preserve">M</id> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
3.
求解矩陣的面積。
<region id="ID0EYXVGB" actualWidth="126.63333333333334" actualHeight="62.800000000000004" top="384.00000000000006" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="18"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <pow /> <id xml:space="preserve">M</id> <real>2</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
4.
逆轉矩陣。
<region id="ID0EIZVGB" actualWidth="200.29666666666665" actualHeight="62.800000000000004" top="499.20000000000005" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="19"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <pow /> <id xml:space="preserve">M</id> <real>-1</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
5.
顯示將矩陣乘以其在單位矩陣中的逆轉結果
<region id="ID0EY1VGB" actualWidth="138.72000000000003" actualHeight="62.800000000000004" top="614.40000000000009" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="20"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <mult /> <id xml:space="preserve">M</id> <apply> <pow /> <id xml:space="preserve">M</id> <real>-1</real> </apply> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
求解線性系統
1.
定義向量。
<region id="ID0EV3VGB" actualWidth="66.923333333333346" actualHeight="62.800000000000004" top="787.20000000000016" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="21"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">v</id> <matrix rows="3" cols="1"> <real>13</real> <real>-3</real> <real>50</real> </matrix> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
2.
求解線性系統
Mx = v
。
<region id="ID0EJ5VGB" actualWidth="78.166666666666671" actualHeight="27.752000000000002" top="902.40000000000009" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="22"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">x</id> <apply> <mult /> <apply> <pow /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id> <real>-1</real> </apply> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">v</id> </apply> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EX5VGB" actualWidth="94.886666666666684" actualHeight="62.800000000000004" top="960.00000000000011" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="23"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id xml:space="preserve">x</id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
3.
顯示在
M
乘以
x
時，傳回的原始向量
v
。
<region id="ID0ETAWGB" actualWidth="98.240000000000009" actualHeight="62.800000000000004" top="1075.2000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="24"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <mult /> <id xml:space="preserve">M</id> <id xml:space="preserve">x</id> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
巢狀陣列
1.
定義巢狀陣列。
<region id="ID0EQCWGB" actualWidth="47.643333333333338" actualHeight="36.800000000000004" top="1209.6000000000001" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="25"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="*" xml:space="preserve">α</id> <real>0</real> </apply> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">v</id> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0E5CWGB" actualWidth="54.243333333333339" actualHeight="36.800000000000004" top="1248.0000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="26"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="*" xml:space="preserve">α</id> <real>1</real> </apply> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
2.
顯示巢狀陣列。
<region id="ID0EOEWGB" actualWidth="111.84" actualHeight="118.60000000000001" top="1363.2000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="27"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id xml:space="preserve">α</id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="true" /> </resultFormat> </math> </region>
3.
從巢狀陣列萃取矩陣。
<region id="ID0E5FWGB" actualWidth="80.63333333333334" actualHeight="62.800000000000004" top="1516.8000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="28"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id xml:space="preserve">α</id> <real>0</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EMGWGB" actualWidth="101.84333333333333" actualHeight="62.800000000000004" top="1593.6000000000001" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="29"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id xml:space="preserve">α</id> <real>1</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
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