Difference between revisions of "Invert Command"
From GeoGebra Manual
m (fixed spacing) |
|||
Line 3: | Line 3: | ||
;Invert[ <Matrix> ] | ;Invert[ <Matrix> ] | ||
: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}-2 & 1\\1.5 & -0.5\end{pmatrix}</math>, the inverse matrix of <math>\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}</math>.}} |
− | <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>.}} | ||
;Invert[ <Function> ] | ;Invert[ <Function> ] | ||
:Gives the inverse of the function. | :Gives the inverse of the function. | ||
Line 13: | Line 12: | ||
;Invert[ <Matrix> ] | ;Invert[ <Matrix> ] | ||
: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}\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>}} |
− | <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. | ||
− | :{{ | + | :{{examples|1=<div> |
:*<code><nowiki>Invert[(x + 1) / (x + 2)]</nowiki></code> yields ''<math>\frac{-2x + 1}{x - 1}</math>''. | :*<code><nowiki>Invert[(x + 1) / (x + 2)]</nowiki></code> yields ''<math>\frac{-2x + 1}{x - 1}</math>''. | ||
:*<code><nowiki>Invert[x^2 + 2 x + 1]</nowiki></code> yields ''<math>\sqrt x - 1</math>''.</div>}} | :*<code><nowiki>Invert[x^2 + 2 x + 1]</nowiki></code> yields ''<math>\sqrt x - 1</math>''.</div>}} | ||
:{{note|1=In the [[CAS_View|CAS View]], the command also works if the function contains more than one ''x''.}} | :{{note|1=In the [[CAS_View|CAS View]], the command also works if the function contains more than one ''x''.}} |
Revision as of 11:07, 19 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.
- Examples:
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.