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.
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.
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