Manuals/calci/MINVERSE

MINVERSE(a)

• $a$ is the array of numeric elements.
  • MINVERSE(), returns the matrix inverse of an array.

Description

• This function gives the inverse matrix for the given matrix.
• We have to find a inverse of a matrix then it should satisfy the following conditions
• 1.A matrix must be a square matrix.
• 2.It's determinant not equal to 0.
• Let $A$ be the 2x2 matrix with the elements

$A={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}$.

• Then the inverse of matrix $A$ is denoted by $A^{-1}$.

$A^{-1}={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}^{-1}={\frac {1}{ad-bc}}*{\begin{bmatrix}d&-b\\-c&a\\\end{bmatrix}}$

• Now let $A$ be the matrix is of order $nXn$.
• Then the inverse of 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 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}= \frac{1}{det(A)}*adj(A)}
• Where 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 adj(A)} is the adjoint of 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} .
• Adjoint is the matrix formed by taking the Transpose of the Co-factor matrix of the original matrix.
• 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 A.A^{-1}=A^{-1}.A = I} , where 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 I} is the identity matrix.
• Non-square matrices do not have inverses.
• Not all square matrices have inverses.
• A square matrix which has an inverse is called invertible or non-singular, and a square matrix without an inverse is called non-invertible or singular.
• This function will return the result as error when

1. Any one of the cell is non-numeric or any cell is empty or contain text
2. Suppose number of rows not equal to number of columns

ZOS

• The syntax is to calculate the inverse of the matrix in ZOS is 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 MINVERSE(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 the array of numeric elements.
• For e.g.,minverse([[10,12],[11,14]])

Examples

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 Matrix A= \begin{bmatrix} 4 & 3 \\ 3 & 2 \\ \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 MINVERSE(B5:C6)= \begin{bmatrix} -2 & 3 \\ 3 & -4 \\ \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 Matrix A= \begin{bmatrix} 3 & 4 \\ 6 & 8 \\ \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 MINVERSE(C4:D5)=Null} , because its determinant value is 0.

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 Matrix A= \begin{bmatrix} 2 & 3 \\ 4 & 7 \\ \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 MINVERSE(B4:C5)= \begin{bmatrix} 3.5 & -1.5 \\ -2 & 1 \\ \end{bmatrix} }

Related Videos

Inverse of Matrix

See Also

• MMULT
• MDETERM

References

• Matrix Inverse

• List of Main Z Functions

• Z3 home