# HOW TO IDENTIFY IF THE GIVEN MATRIX IS SINGULAR OR NONSINGULAR

## About "How to Identify If the Given Matrix is Singular or Nonsingular"

How to Identify If the Given Matrix is Singular or Nonsingular :

Here we are going to see, how to check if the given matrix is singular or non singular.

A square matrix A is said to be singular if |A| = 0. A square matrix A is said to be non-singular if | A | ≠ 0.

## How to Identify If the Given Matrix is Singular or Nonsingular - Practice questions

Question 1 :

Identify the singular and non-singular matrices:

Solution :

In order to check if the given matrix is singular or non singular, we have to find the determinant of the given matrix.

 = 1[45-48]-2[36-42]+3[32-35]  =  1[-3] - 2[-6] + 3[-3]  =  -3 + 12 - 9  =  0

Hence the matrix is singular matrix.

Solution :

 =  2[0-20]+3[42-4]+5[30-0]  =  2(-20) + 3(38) + 5(30)  =  -40 + 84 + 150  =  194

It is not equal to zero. Hence it is non singular matrix.

Solution :

Since the given matrix is skew matrix, |A|  =  0.

Hence it is singular matrix.

Question 2 :

Determine the values of a and b so that the following matrices are singular:

Since it is singular matrix, |A|  =  0

|A|  =  7a - (-6)  =  0

7a + 6  =  0

7a  =  -6

a  =  -6/7

Hence the value of a is -6/7.

Solution :

Since it is singular matrix, |B|  =  0

|B|  =  (b- 1)[4 + 4] - 2[12 - 2] + 3[-6 - 1]

(b - 1)(8) - 2(10) + 3(-7)  =  0

8(b - 1) - 20 - 21  =  0

8(b - 1) - 41  =  0

8(b-1)  =  41

b-1  =  41/8

b  =  (41/8) + 1

=  (41 + 8)/8  =  49/8

Hence the value of B is 49/8.

Question 3 :

If cos 2 θ = 0 , determine

Solution :

cos 2 θ = 0

2θ = cos-1(0 )

2θ = 90 degree

θ  =  90/2  =  45 degree

To multiply the above determinants, let us use row by column rule.

=  1(1 - sin2θcos2θ) - sinθcosθ(sinθcosθ-sin2θcos2θ) + sinθcosθ(sin2θcos2θ-sinθcosθ)

=  1 - sin2θcos2θ - sin2θcos2θ + sin3θcos3θ + sin3θcos3θ - sin2θcos2θ

=  1 - 3sin2θcos2θ + 2sin3θcos3θ

=  1 - 3(sinθcosθ)2 + 2(sinθcosθ)3

By applying 45 degree instead of θ, we get

=  1 - 3(sin 45 cos 45)+ 2(sin 45 cos 45)3

=  1 - 3((1/2)(1/2))+ 2((1/2)(1/2))3

=  1 - 3(1/4) + 2(1/8)

=  1 - (3/4) + (1/4)

=  (4 - 3 + 1)/4

=  2/4  =  1/2

Question 4 :

Find the value of product

Solution :

In order to find the square of the given determinant, we have to multiply the given determinant by the same.

Here we have followed row by column multiplication.

=  21 - 15

=  6

After having gone through the stuff given above, we hope that the students would have understood, "How to Identify If the Given Matrix is Singular or Nonsingular".

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