Manuals/calci/MINVERSE

MINVERSE(arr)

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

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

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

$MatrixA={\begin{bmatrix}4&3\\3&2\\\end{bmatrix}}$ $MINVERSE(B5:C6)={\begin{bmatrix}-2&3\\3&-4\\\end{bmatrix}}$

$MatrixA={\begin{bmatrix}3&4\\6&8\\\end{bmatrix}}$ $MINVERSE(C4:D5)=Null$ , because its determinant value is 0.

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