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.
Searched about 1,900 times a month in IndiaSolve a similar doubt →
Stuck on something else?
Type your own doubt into the solver and get the full working in seconds — free, for physics, chemistry, maths and biology.
Open the solverRelated doubts