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Singular Matrices
A matrix with a determinant of zero is called singular, and cannot be inverted.
When the Determinant Is Zero
A later lesson finds a matrix's inverse using a formula that divides by the determinant. Dividing by is impossible — which is exactly why a singular matrix (determinant ) has no inverse.
Example 1 — confirming a singular matrix
Is A = singular?
- det(A) = () − () =
Answer: Yes, A is singular (its determinant is )
Example 2 — a non-singular matrix
Is A = singular?
- det(A) = () − () =
Answer: No — the determinant is , not , so A is not singular and does have an inverse.
Practice
Which of these matrices is singular?
More lessons in Matrices and Determinants · Next: The Determinant of a 3×3 Matrix · Previous: The Determinant of a 2×2 Matrix