Difference between revisions of "Invert Command"

From GeoGebra Manual
Jump to: navigation, search
(changed CAS syntax description)
m (nicer note formatting)
 
(4 intermediate revisions by 3 users not shown)
Line 1: Line 1:
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
;Invert[ <Matrix> ]
+
;Invert( <Matrix> )
 
: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.
+
:{{note|In the [[File:Menu view cas.svg|link=|16px]] [[CAS_View|CAS View]] undefined 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>}}
+
:{{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.  
:{{example|1=<div><code><nowiki>Invert[sin(x)]</nowiki></code> yields ''asin(x)''.</div>}}
+
:{{example|1=<div><code><nowiki>Invert(sin(x))</nowiki></code> yields ''asin(x)''.</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>
 
:{{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>}}}}
:{{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=<div>
 +
*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''.
 +
* See also [[Eigenvalues Command]], [[Eigenvectors Command]], [[SVD Command]], [[Transpose Command]], [[JordanDiagonalization Command]]
 +
</div>}}

Latest revision as of 08:06, 29 June 2018


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 Menu view cas.svg CAS View undefined 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))) and Invert(CompleteSquare(x^2 + 2 x + 1)) yield the inverse functions.


Note:
© 2024 International GeoGebra Institute