Manuals/calci/MINVERSE

MINVERSE(arr)

• $arr$ is the array of numeric elements

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 $A$ is $A^{-1}={\frac {1}{det(A)}}*adj(A)$
• Where $adj(A)$ is the adjoint of $A$.
• Adjoint is the matrix formed by taking the Transpose of the Co-factor matrix of the original matrix.
• Also $A.A^{-1}=A^{-1}.A=I$, where $I$ 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

Examples

$MatrixA={\begin{bmatrix}4&3\\3&2\\\end{bmatrix}}$ 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} }

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)=<math>Matrix A= \begin{bmatrix} 3.5 & -1.5 \\ -2 & 1 \\ \end{bmatrix} }

See Also

• COS
• TAN
• ASIN
• DSIN

References

• List of Trigonometric Functions
• SIN