State whether the matrix [(2, 3)(6, 4)] is singular or non-singular.

Question

State whether the matrix \(\begin{bmatrix} 2 & 3 \\ 6 & 4 \\ \end{bmatrix}\) is singular or non-singular.

Answer 1

Let A = \(\begin{bmatrix} 2 & 3 \\ 6 & 4 \\ \end{bmatrix}\)

Then |A| = \(\begin{bmatrix} 2 & 3 \\ 6 & 4 \\ \end{bmatrix}\)

= 2 × 4 - 3 × 6

= -10 (Expanding along R₁)

Since |A| ≠ 0, therefore A is a non-singular matrix.