Difference between revisions of "Invert Command"
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}} |
| − | {{command|cas=true|vector-matrix}} | + | ;Invert( <Matrix> ) |
| − | ;Invert | ||
:Inverts the given matrix. | :Inverts the given matrix. | ||
| − | :{{example|1= | + | :{{example|1=<code><nowiki>Invert({{1, 2}, {3, 4}})</nowiki></code> yields <math>\begin{pmatrix}-2 & 1\\1.5 & -0.5\end{pmatrix}</math>, the inverse matrix of <math>\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}</math>.}} |
| − | \begin{pmatrix} | + | :{{note|In the [[File:Menu view cas.svg|link=|16px]] [[CAS_View|CAS View]] undefined variables are allowed too. |
| − | -2 & 1\\ | + | :{{example|1=<div><code><nowiki>Invert({{a, b}, {c, d}})</nowiki></code> yields <math>\begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ ad- bc}\end{pmatrix}</math>, the inverse matrix of <math>\begin{pmatrix}a & b\\c & d\end{pmatrix}</math>.</div>}} |
| − | 1.5 & -0.5 | ||
| − | \end{pmatrix} | ||
| − | </math>, | ||
| − | \begin{pmatrix} | ||
| − | 1 & 2\\ | ||
| − | 3 & 4 | ||
| − | \end{pmatrix} | ||
| − | </math>. | ||
| − | = | ||
| − | |||
| − | |||
| − | :{{example|1=<div><code><nowiki>Invert | ||
| − | \begin{pmatrix} | ||
| − | \frac{d}{ | ||
| − | \frac{-c}{ | ||
| − | \end{pmatrix} | ||
| − | </math> the inverse matrix of <math> | ||
| − | \begin{pmatrix} | ||
| − | a & b\\ | ||
| − | c & d | ||
| − | \end{pmatrix} | ||
| − | </math>.</div> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | }} | ||
}} | }} | ||
| + | ;Invert( <Function> ) | ||
| + | :Gives the inverse of the function. | ||
| + | :{{example|1=<div><code><nowiki>Invert(sin(x))</nowiki></code> yields ''asin(x)''.</div>}} | ||
| + | :{{note|1=<div>The function must contain just one ''x'' and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x). <br>If there is more than one ''x'' in the function another command might help you:</div> | ||
| + | ::{{example|1=<div>Both <code><nowiki>Invert(PartialFractions((x + 1) / (x + 2)))</nowiki></code> and <code><nowiki>Invert(CompleteSquare(x^2 + 2 x + 1))</nowiki></code> yield the inverse functions.</div>}}}} | ||
| + | |||
| + | |||
| + | {{note|1=<div> | ||
| + | *In the [[File:Menu view cas.svg|link=|16px]] [[CAS_View|CAS View]], the command also works if the function contains more than one ''x''. | ||
| + | * See also [[Eigenvalues Command]], [[Eigenvectors Command]], [[SVD Command]], [[Transpose Command]], [[JordanDiagonalization Command]] | ||
| + | </div>}} | ||
Latest revision as of 09:06, 29 June 2018
- Invert( <Matrix> )
- Inverts the given matrix.
- Example:
Invert({{1, 2}, {3, 4}})yields \begin{pmatrix}-2 & 1\\1.5 & -0.5\end{pmatrix}, the inverse matrix of \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}.
- Note: In the
CAS View undefined variables are allowed too. - Example:
Invert({{a, b}, {c, d}})yields \begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ ad- bc}\end{pmatrix}, the inverse matrix of \begin{pmatrix}a & b\\c & d\end{pmatrix}.
- Invert( <Function> )
- Gives the inverse of the function.
- Example:
Invert(sin(x))yields asin(x).
- Note:The function must contain just one x and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x).
If there is more than one x in the function another command might help you:- Example:Both
Invert(PartialFractions((x + 1) / (x + 2)))andInvert(CompleteSquare(x^2 + 2 x + 1))yield the inverse functions.
Note:
- In the CAS View, the command also works if the function contains more than one x.
- See also Eigenvalues Command, Eigenvectors Command, SVD Command, Transpose Command, JordanDiagonalization Command
