A matrix is singular if its determinant is equal to 0. A 3x3 matrix is provided as an example of a singular matrix, where the calculation of the determinant equals 0. Therefore, this matrix is singular. A second example shows that if a 2x1 matrix is pre-multiplied by a singular 2x2 matrix, then the value of x must be 0.

2. Singular Matrix
If the determinant of a matrix is zero, then the matrix is called a singular
matrix, otherwise non-singular matrix.
Example-8:
If
4 8 6
2 5 3
2 4 3
A =
 
 
 
  
find A
Solution:
4 8 6
2 5 3
2 4 3
A =
A
5 3 2 3 2 5
4 8 6
4 3 2 3 2 4
= − +
4(15 12) 8(6 6) 6(8 10)A = − − − + −
A 4(3) 8(0) 6( 2)= − + −
A =12 – 0 – 12
A = 12 – 12
A = 0
The given matrix is a singular matrix.

3. Example-9:
5 5
a singular matrix then find the value of x
2
IF A is
x
 
=  
 
Solution:
5 5
2
10 5
0 10 5
5 10
10
5
2
A
x
A x
x
x
x
x
=
= −
= −
=
=
=