Question

Which of the following matrices are singular or non singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`

Answer 1

Let A = `[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`

∴ |A| = `|(5, 0, 5),(1, 99, 100),(6, 99, 105)|`

Applying C₂ → C₂ + C₁, we get

|A| = `|(5, 5, 5),(1, 100, 100),(6, 105, 105)|`

= 0         ...[∵ C₂ and C₃ are identical]

∴ A is a singular matrix.