Difference between revisions of "Invert Command"
From GeoGebra Manual
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| Line 4: | Line 4: | ||
:Inverts the given matrix. | :Inverts the given matrix. | ||
:{{example|1=<code><nowiki>Invert[{{1, 2}, {3, 4}}]</nowiki></code> yields | :{{example|1=<code><nowiki>Invert[{{1, 2}, {3, 4}}]</nowiki></code> yields | ||
| − | <math>\begin{pmatrix} | + | <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>.}} |
| − | -2 & 1\\ | ||
| − | 1.5 & -0.5 | ||
| − | \end{pmatrix} | ||
| − | </math>, the inverse matrix of <math>\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}</math>.}} | ||
;Invert[ <Function> ] | ;Invert[ <Function> ] | ||
:Gives the inverse of the function. | :Gives the inverse of the function. | ||
| Line 18: | Line 14: | ||
:Inverts the given matrix. | :Inverts the given matrix. | ||
:{{example|1=<div><code><nowiki>Invert[{{a, b}, {c, d}}]</nowiki></code> yields | :{{example|1=<div><code><nowiki>Invert[{{a, b}, {c, d}}]</nowiki></code> yields | ||
| − | <math>\begin{pmatrix} | + | <math>\begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ ad- bc}\end{pmatrix}</math> |
| − | \frac{d}{ad- bc} & \frac{-b}{ad- bc}\\ | + | , the inverse matrix of <math>\begin{pmatrix}a & b\\c & d\end{pmatrix} |
| − | \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>}} | </math>.</div>}} | ||
;Invert[ <Function> ] | ;Invert[ <Function> ] | ||
Revision as of 09:44, 17 April 2015
- 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}.
- 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.
CAS Syntax
- Invert[ <Matrix> ]
- Inverts the given matrix.
- 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[(x + 1) / (x + 2)]yields \frac{-2x + 1}{x - 1}.Invert[x^2 + 2 x + 1]yields \sqrt x - 1.
- Note: In the CAS View, the command also works if the function contains more than one x.
