Question

Without expanding evaluate the following determinant:

`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`

Answer 1

Let D = `|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`

Applying C₃ → C₃ – 9C₂, we get

D = `|(2, 7, 2),(3, 8, 3),(5, 9, 5)|`

= 0      ...[∵ C₁ and C₃ are identical]