Singular Matrix

If the determinant of a matrix is 0 then the matrix has no inverse. Such a matrix is called a singular matrix.

The following diagrams show how to determine if a 2×2 matrix is singular and if a 3×3 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?

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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?

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Determine A Value In A 2×2 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.

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Singular Matrices Examples

1. Determine whether or not there is a unique solution.
2. For what value of x is A a singular matrix.

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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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