Difference between revisions of "Invert Command"
From GeoGebra Manual
m |
m |
||
Line 8: | Line 8: | ||
1.5 & -0.5 | 1.5 & -0.5 | ||
\end{pmatrix} | \end{pmatrix} | ||
− | </math>, the inverse matrix of <math> | + | </math>, the inverse matrix of <math>\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}</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 21: | Line 17: | ||
;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 <math> | + | :{{example|1=<div><code><nowiki>Invert[{{a, b}, {c, d}}]</nowiki></code> yields |
− | \begin{pmatrix} | + | <math>\begin{pmatrix} |
\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\ | \frac{d}{ad- bc} & \frac{-b}{ad- bc}\\ | ||
\frac{-c}{ad- bc}& \frac{a}{ ad- bc} | \frac{-c}{ad- bc}& \frac{a}{ ad- bc} | ||
− | \end{pmatrix} | + | \end{pmatrix}</math> |
− | </math>, the inverse matrix of <math> | + | , the inverse matrix of <math> |
\begin{pmatrix} | \begin{pmatrix} | ||
a & b\\ | a & b\\ |
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.