Difference between revisions of "Invert Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
{{command|cas=true|vector-matrix}}
 
 
;Invert[ <Matrix> ]
 
;Invert[ <Matrix> ]
 
:Inverts the given matrix.
 
:Inverts the given matrix.
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:*<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''.}}
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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''.}}

Revision as of 12:33, 5 August 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)]] and Invert[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 Menu view cas.svg CAS View, the command also works if the function contains more than one x.
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