Difference between revisions of "Invert Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude> | <noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude> | ||
{{command|cas=true|vector-matrix}} | {{command|cas=true|vector-matrix}} | ||
− | ; Invert[Matrix]: Inverts the given matrix. | + | ;Invert[ <Matrix> ] |
− | : {{ | + | :Inverts the given matrix. |
+ | :{{example|1=<div><code><nowiki>Invert[{{1, 2}, {3, 4}}]</nowiki></code> yields <math> | ||
\begin{pmatrix} | \begin{pmatrix} | ||
-2 & 1\\ | -2 & 1\\ | ||
1.5 & -0.5 | 1.5 & -0.5 | ||
+ | \end{pmatrix} | ||
+ | </math>, the the inverse matrix of <math> | ||
+ | \begin{pmatrix} | ||
+ | 1 & 2\\ | ||
+ | 3 & 4 | ||
\end{pmatrix} | \end{pmatrix} | ||
</math>.</div>}} | </math>.</div>}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
− | ;Invert[Matrix]: Inverts the given matrix. | + | ;Invert[ <Matrix> ] |
− | :{{example|1=<div><code><nowiki>Invert[{{a, b}, {c, d}}]</nowiki></code> | + | :Inverts the given matrix. |
+ | :{{example|1=<div><code><nowiki>Invert[{{a, b}, {c, d}}]</nowiki></code> yields <math> | ||
\begin{pmatrix} | \begin{pmatrix} | ||
\frac{d}{a* d- b* c} & \frac{-b}{a* d- b* c}\\ | \frac{d}{a* d- b* c} & \frac{-b}{a* d- b* c}\\ | ||
\frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c} | \frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c} | ||
+ | \end{pmatrix} | ||
+ | </math> the inverse matrix of <math> | ||
+ | \begin{pmatrix} | ||
+ | a & b\\ | ||
+ | c & d | ||
\end{pmatrix} | \end{pmatrix} | ||
</math>.</div>}} | </math>.</div>}} | ||
− | |||
{{betamanual|version=4.2| | {{betamanual|version=4.2| | ||
1=; Invert[ <Function> ] | 1=; Invert[ <Function> ] |
Revision as of 12:21, 17 September 2012
- Invert[ <Matrix> ]
- Inverts the given matrix.
- Example:
Invert[{{1, 2}, {3, 4}}]
yields\begin{pmatrix} -2 & 1\\ 1.5 & -0.5 \end{pmatrix} , the the inverse matrix of
\begin{pmatrix} 1 & 2\\ 3 & 4 \end{pmatrix}
.CAS Syntax
- Invert[ <Matrix> ]
- Inverts the given matrix.
- Example:
Invert[{{a, b}, {c, d}}]
yields\begin{pmatrix} \frac{d}{a* d- b* c} & \frac{-b}{a* d- b* c}\\ \frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c} \end{pmatrix} the inverse matrix of
\begin{pmatrix} a & b\\ c & d \end{pmatrix}
.Following text is about a feature that is supported only in GeoGebra 4.2.
- Invert[ <Function> ]
- Returns the inverse of the function.
Note: The function must contain just one x and no account is taken of domain or range, eg 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:
Invert[PartialFractions[(x+1)/(x+2)]]
orInvert[CompleteSquare[x^2+2x+1]]
gives you the inverse of the function.