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Maths for Engineers - 1

Nonsingular Matrix

Nonsingular Matrix:

A square n \times \!\, n matrix A is said to be non singular or invertible if there is another n \times \!\, n matrix B such that;

In this case the matrix B is called the inverse of A and is commonly denoted by A-1 rather than B. Otherwise the matrix A is called singular or non invertible.

 

Example:1

Since AB = BA = I2, we conculde that B is the inverse of A.

Proof:

Because of these uniqueness, we write the inverse of a non singular matrix A as A-1

 

Exampel-2: Consider

                                 

Equating corresponding entries of these two matrices;

Since the matrix is;

                    

   

We conclude that A is non singular matrices;