Manuals/calci/MINVERSE

MINVERSE(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

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

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

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

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

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

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