Difference between revisions of "Manuals/calci/MATRIXINVERSE"
| Line 13: | Line 13: | ||
a & b \\ | a & b \\ | ||
c & d | c & d | ||
| − | \end{bmatrix}}^{-1}</math>=<math>1 | + | \end{bmatrix}}^{-1}</math>=<math>\frac{1}{det A }\begin{bmatrix} |
d & -b \\ | d & -b \\ | ||
-c & a | -c & a | ||
| − | \end{bmatrix}</math> = | + | \end{bmatrix}</math> =\frac{1}{ad-bc} \begin{bmatrix} |
d & -b \\ | d & -b \\ | ||
-c & a | -c & a | ||
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
| + | *Consider 3x3 matrix A and its inverse is calculated by | ||
| + | <math>A^{-1}={\begin{bmatrix} | ||
| + | a & b & c \\ | ||
| + | d & e & f \\ | ||
| + | g & h & i | ||
| + | \end{bmatrix}}^{-1}</math>=<math>\frac{1}{det A }{\begin{bmatrix} | ||
| + | A & B & C \\ | ||
| + | D & E & F \\ | ||
| + | G & H & I | ||
| + | \end{bmatrix}}^T </math>= <math>\frac{1}{det A } {\begin{bmatrix} | ||
| + | A & D & G \\ | ||
| + | B & E & H \\ | ||
| + | C & F & I | ||
| + | \end{bmatrix}}</math> | ||
Revision as of 17:12, 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 \frac{1}{det A }\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}} =\frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}</math>
- Consider 3x3 matrix A and its inverse 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 & e & f \\ g & h & i \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 \frac{1}{det A }{\begin{bmatrix} A & B & C \\ D & E & F \\ G & H & I \end{bmatrix}}^T } = 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 \frac{1}{det A } {\begin{bmatrix} A & D & G \\ B & E & H \\ C & F & I \end{bmatrix}}}