Question

Without expanding evaluate the following determinant:

`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`

Answer 1

Let D = `|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`

Taking (3x) common from R₃, we get

D = `3x|(2, 3, 4),(5, 6, 8),(2, 3, 4)|`

= (3x)(0)          ...[∵ R₁ and R₃ are identical]
= 0