CBSEJEEClass 12

What is a singular matrix?

Answer

A singular matrix is a square matrix whose determinant is zero, and therefore it does not have an inverse.

The working

Definition

A square matrix A is called singular if its determinant |A| = 0.

No inverse

Since the inverse is A⁻¹ = adj(A)/|A|, a zero determinant makes the inverse undefined, so a singular matrix is non-invertible.

Contrast

A matrix with a non-zero determinant is called non-singular and always has a unique inverse.

Example

The matrix [[1, 2], [2, 4]] has determinant (1)(4) − (2)(2) = 0, so it is singular.

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