Concept

Singular Matrix

A singular matrix is a matrix whose determinant is zero.

A is a singular matrix ⇕ det (A)=0

Since its determinant is zero, a singular matrix has no inverse.

Example

Consider a 2 * 2 matrix A. A = 2 & 6 1 & 3 Whether a matrix is singular depends on its determinant.

|A|=det 2 & 6 1 & 3

▼

Simplify right-hand side

Calculate the determinant of a 2 * 2 matrix

|A|=2(3)-6(1)

Multiply

|A|=6-6

SubTerm

Subtract term

|A|=0

Since its determinant is zero, A is a singular matrix.

Extra

Why Do We Calculate the Determinant

A link between the determinant and the the inverse of a non-singular matrix can be illustrated in the formula for the inverse of a 2 * 2 matrix. A=[ cc a & b c & d ] ⇓ A^(- 1)=1/det (A) [ cc d & - b - c & a ] The determinant is in a denominator. Therefore, the formula is well defined if and only if the determinant is not zero.

Example

Extra

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