**MATHS :: Lecture 21 :: Solving simulteneous equation and cramers rule**

__ __

**INVERSE OF A MATRIX**

**Definition**

Let A be any square matrix. If there exists another square matrix B Such that AB = BA = I (I is a unit matrix) then B is called the inverse of the matrix A and is denoted by A-1.

The cofactor method is used to find the inverse of a matrix. Using matrices, the solutions of simultaneous equations are found.

Introduction to Vectors

Vector Transformations

Vector Dot Product and Vector Length

Unit Vectors

Matrix Vector Products

Matrices to solve a vector combination problem

Converting a line from Cartesian to vector form

Working Rule to find the inverse of the matrix

Step 1: Find the determinant of the matrix.

Step 2: If the value of the determinant is non zero proceed to find the inverse of the matrix.

Step 3: Find the cofactor of each element and form the cofactor matrix.

Step 4: The transpose of the cofactor matrix is the adjoint matrix.

Step 5: The inverse of the matrix A-1 =

Example

Find the inverse of the matrix

Solution

Let A =

Step 1

Step 2

The value of the determinant is non zero

\A-1 exists.

Step 3

Let Aij denote the cofactor of

*aij*in

Step 4

The matrix formed by cofactors of element of determinant is

\adj A =

Step 5

=

Download this lecture as PDF here |