Manuals/calci/MATRIXINVERSE

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 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)} , $a$ 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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {1}{detA}}{\begin{bmatrix}A&D&G\\B&E&H\\C&F&I\end{bmatrix}}}