For what value of x is the matrix singular?

We are given that,

is singular matrix.

We need to find the value of x.

Let us recall the definition of singular matrix.

A singular matrix is a square matrix that doesn’t have a matrix inverse. A matrix ‘A’ is singular iff its determinant is zero, i.e., |A| = 0.

Hence, we just need to find the determinant of the given matrix and equate it to zero.

Determinant of 2 × 2 matrix is found as,

So,

Now, equate this to 0.

That is,

⇒ 3x – 6 = 0

⇒ 3x = 6

⇒ x = 2

Thus, the value of x = 2 for which the matrix is singular.