HOW TO CHECK WHETHER THE MATRIX IS INVERTIBLE OR NOT

A square matrix whose determinant is 0 is called singular matrix.

|A| ≠ 0

To check if the function is invertible or not, we have to follow the steps.

i) Let us consider the given matrix as A.

ii) Finding (|A|) determinant of A.

iii) If |A| ≠ 0, then the given matrix is non singular and it is not invertible. Inverse does not exists.

iv) If |A| = 0, then the given matrix is singular matrix and it is invertible.

Identify the singular and non-singular matrix.

Problem 1 :

Solution:

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

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

Problem 2 :

Solution:

Hence the matrix is singular matrix.

Problem 3 :

Solve:

Solution:

Problem 4 :

Solution:

Problem 5 :

Solution:

Taking out 2 common from C_3.

If any two row or column are identical then value of determinant is zero.

Here C₁ and C₃ are identical.

= 2 × 0

= 0

Hence the determinant of given is zero by calculating without usual expansion.

Problem 6 :

Solve:

Solution:

Since, all the entries below the principal diagonal are zero, the value of the determinant is (x - 1)(x - 2)(x -3) = 0 which gives x = 1, 2, 3.

Problem 7 :

Solution:

Problem 8 :

Solution:

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