What is Non-Singular Matrix?

A non-singular matrix is a matrix with non-zero determinant. The matrices whose determinant is not equal to zero are known as non-singular matrices. The condition for a matrix to be non-singular is that the determinant of the matrix should be non-zero. The condition for a non-singular matrix can be mathematically represented as Det (Matrix) ≠ 0 or |Matrix| ≠ 0. The singular matrices have an inverse, so they are also called invertible matrices.

Non-Singular Matrix Definition

A square matrix whose determinant is non-zero is referred to as non-singular matrix. In other words, a square matrix with its determinant not equal to zero is called as non-singular matrix.

If |A| ≠ 0 then, A is non-singular matrix

Non-Singular Matrix Example

Some examples of non-singular matrix are:

Example: Check the matrix C = [Tex]\begin{bmatrix} 5&6& 0\\ 4& 2 & 3\\ 1 & 10& 9 \end{bmatrix}[/Tex] is a non-singular matrix or not?

Solution:

First, we find determinant of C i.e., |C| = [Tex]\begin{vmatrix} 5&6& 0\\ 4& 2 & 3\\ 1 & 10& 9 \end{vmatrix}[/Tex]

|C| = 5 × [(2 × 9) – (3 × 10)] – 6 × [(9 × 4) – (3 × 1)] + 0 × [(4 × 10) – (2 × 1)]

|C| = 5 × [18 – 30] – 6 × [36 – 3] + 0

|C| = 5 × (-12) – 6 × (33)

|C| = -60 – 198

|C| = -258

Since, |C| is not equal to zero the given matrix C is a non-singular matrix.

Example: Check whether the matrix A = [Tex]\begin{bmatrix} 10 & 7\\ 4 & 2 \end{bmatrix}[/Tex] is singular or non-singular?

Solution:

First, we find the determinant of A i.e., |A| = [Tex]\begin{bmatrix} 10 & 7\\ 4 & 2 \end{bmatrix}[/Tex]

|A| = (2 × 10) – (7 × 4)

|A| = 20 – 28

|A| = -8

Since, |A| is not equal to zero the given matrix A is non-singular matrix.

Non-singular matrix is a square whose determinant is not zero. The non-singular matrices are also invertible matrices. In this article we will explore non-singular matrix in detail along with the non-singular matrix definition, non-singular matrix examples. We will also discuss how to find a matrix is non-singular or not, properties of non-singular matrix and solve some examples related to non-singular matrix. Let’s start our learning on the topic “Non-Singular Matrix”.