Related Pages
Types Of Matrices
More On Singular Matrices
More Lessons On Matrices
These lessons help Algebra students to learn what a singular matrix is and how to tell whether a matrix is singular.
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.
How to know if a matrix is invertible?
How to know if a 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?
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.
Example: Determine the value of a that makes matrix A singular.
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.