Difference between revisions of "Invert Command"

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\frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c}
 
\frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c}
 
\end{pmatrix}
 
\end{pmatrix}
</math> the inverse matrix of <math>
+
</math>, the inverse matrix of <math>
 
\begin{pmatrix}
 
\begin{pmatrix}
 
a & b\\
 
a & b\\
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\end{pmatrix}
 
\end{pmatrix}
 
</math>.</div>}}
 
</math>.</div>}}
{{betamanual|version=4.2|
+
;Invert[ <Function> ]
1=; Invert[ <Function> ]
+
:Gives the inverse of the function.  
: Returns the inverse of the function.  
+
:{{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). If there is more than one ''x'' in the function another command might help you:</div>
{{Note|1=The function must contain just one ''x'' and no account is taken of domain or range, eg for f(x)=x^2 or f(x) = sin(x).  
+
::{{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>}}}}
If there is more than one ''x'' in the function another command might help you:
 
:{{example|1=<div><code><nowiki>Invert[PartialFractions[(x+1)/(x+2)]]</nowiki></code> or <code><nowiki>Invert[CompleteSquare[x^2+2x+1]]</nowiki></code> gives you the inverse of the function.</div>}}
 
}}
 
}}
 

Revision as of 12:43, 17 September 2012


Invert[ <Matrix> ]
Inverts the given matrix.
Example:
Invert[{{1, 2}, {3, 4}}] yields

\begin{pmatrix} -2 & 1\\ 1.5 & -0.5 \end{pmatrix} , the the inverse matrix of

\begin{pmatrix} 1 & 2\\ 3 & 4 \end{pmatrix}

.

CAS Syntax

Invert[ <Matrix> ]
Inverts the given matrix.
Example:
Invert[{{a, b}, {c, d}}] yields

\begin{pmatrix} \frac{d}{a* d- b* c} & \frac{-b}{a* d- b* c}\\ \frac{-c}{a* d- b* c}& \frac{a}{ a* d- b* c} \end{pmatrix} , the inverse matrix of

\begin{pmatrix} a & b\\ c & d \end{pmatrix}

.
Invert[ <Function> ]
Gives the inverse of the function.
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.
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