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

Matrix A A=(4 3

  3     2)

MINVERSE(B5:C6)=(-2 3

                 3       -4)

MATRIX A A=(3 4

     6       8)

MINVERSE(C4:D5)=Null, because its det value is 0. MATRIX A A=(2 3

  4     7)

MINVERSE(B4:C5)=(3.5 -1.5

               -2           1)