Introduction for inverse matrix method

Introduction for inverse matrix method:

The inverse matrix method are formed on the basis like X=A-1B which is formed for finding the matrix X with the equation AX = B It is used in solving the linear system of equations. Here A-1 is the inverse matrix representation. If we have to find the inverse of the 3 x 3 matrix, which uses 2 x 2 matrix for finding the determinant value for the 3 x 3 matrix. If we have to find the inverse of the 4 x 4 matrix, which uses 2 x 2 matrix and 3 x 3 matrix for finding the determinant value for the 4 x 4 matrix.

Definition of INVERSES of MATRICES:

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that [ A A^-1 = I] This can also help us on equations of motion

where I is the identity matrix. A-1to denotes the inverse matrix.

A square matrix A has an inverse if and only if the determinant |A| ≠ 0.

A matrix possessing an inverse is called non singular, or invertible.

In other words, the matrix which when multiplied by the original matrix gives the identity matrix as the solution