Difference between revisions of "Invert Command"
From GeoGebra Manual
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:Inverts the given matrix. | :Inverts the given matrix. | ||
:{{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>.}} | :{{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>.}} | ||
| + | {{note|In the [[File:Menu view cas.svg|link=|16px]] [[CAS_View|CAS View]] undefiened variables are allowed too. | ||
| + | :{{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>}} | ||
| + | }} | ||
;Invert[ <Function> ] | ;Invert[ <Function> ] | ||
:Gives the inverse of the function. | :Gives the inverse of the function. | ||
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:{{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> | :{{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>}}}} | ::{{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>}}}} | ||
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:{{note|1=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''.}} | :{{note|1=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''.}} | ||
Revision as of 12:00, 1 October 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}.
Note: In the 
CAS View undefiened variables are allowed too.
CAS View undefiened 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.
CAS View, the command also works if the function contains more than one x.
