Difference between revisions of "Manuals/calci/MATRIXINVERSE"
(Created page with "<div style="font-size:30px">'''MATRIXINVERSE (a)'''</div><br/> *<math>a</math> is any matrix. ==Description== *This function shows the inverse value of the given matrix. *In ...") |
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a & b \\ | a & b \\ | ||
c & d | c & d | ||
| − | \end{bmatrix}}{-1}</math> | + | \end{bmatrix}}^{-1}</math>=<math>1/det A \begin{bmatrix} |
| + | d & -b \\ | ||
| + | -c & a | ||
| + | \end{bmatrix}</math> =<math> 1/ad-bc \begin{bmatrix} | ||
| + | d & -b \\ | ||
| + | -c & a | ||
| + | \end{bmatrix}</math> | ||
Revision as of 15:55, 20 June 2017
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is any matrix.
Description
- This function shows the inverse value of the given matrix.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MATRIXINVERSE (a)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is any square matrix.
- Inverse of a square matrix is also called reciprocal of a matrix and it is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^-1} .
- Consider the square matrix A has an inverse which should satisfies the following condition Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |A|\ne 0}
- Also Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle AA^{-1}=I} (Identity matrix).
- Consider 2x2 matrix:A=[a b;c d].
- The inverse of matrix A is calculated by
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^{-1}={\begin{bmatrix} a & b \\ c & d \end{bmatrix}}^{-1}} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1/det A \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1/ad-bc \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}}