# Singular Matrix

If the determinant of a matrix is 0 then the matrix has no inverse

It is called a singular matrix.

The following diagrams show how to determine if a 2x2 matrix is singular and if a 3x3 matrix is singular. Scroll down the page for examples and solutions.

Example:

Solution:

Determinant = (3 × 2) – (6 × 1) = 0

The given matrix does not have an inverse. It is a singular matrix.

When a matrix cannot be inverted and the reasons why it cannot be inverted?
How to know if a matrix is invertible?
How to know if a matrix is singular? What is a Singular Matrix and how to tell if a 2x2 Matrix is singular?
A singular matrix is one which is non-invertible i.e. there is no multiplicative inverse, B, such that the original matrix A × B = I (Identity matrix)
A matrix is singular if and only if its determinant is zero.
Example:
Are the following matrices singular?

Determine a Value in a 2x2 Matrix To Make the Matrix Singular
A square matrix A is singular if it does not have an inverse matrix.
Matrix A is invertible (non-singular) if det(A) = 0, so A is singular if det(A) = 0
Example:
Determine the value of b that makes matrix A singular. Singular Matrices Examples
Example:
1. Determine whether or not there is a unique solution.
2. For what value of x is A a singular matrix. Determine a Value in a 3x3 Matrix To Make the Matrix Singular
Example:
Determine the value of a that makes matrix A singular.

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