Matrix Inverse

Calculating the Matrix Inverse for Determinants

Matrix Inverse for Determinants

Matrix Inverse

Determinant of the Matrix

Adjugate Matrix or Matrix of Cofactors

Transpose of the Adjugate Matrix


Steps to Calculate the Matrix Inverse

Matrix Inverse

1. Calculate the determinant of the matrix. If the determinant is zero, the matrix will not inverse.

Determinant of the Matrix

2. The adjugate matrix can be found by replacing every element by its cofactor.

Adjugate Matrix

3.Calculate the transpose of the adjugate matrix.

Transpose of the Adjugate Matrix

4. The matrix inverse is equal to the inverse value of its determinant multiplied by the transpose of the adjugate matrix.

Matrix Inverse


The matrix inverse can also be calculated by the Gaussian elimination method.


Examples

1. Find the inverse matrix:

Inverse Matrix

Inverse Matrix Operations

Inverse Matrix Operations

Inverse Matrix Operations


2. For what values of x in the matrix    Matrix   does the matrix inverse not support?

Inverse Matrix Operations

For x = 0 , Matrix A has no inverse.