Question

Without expanding the determinant, find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`.

Answer 1

Let D = `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`

Applying C₃ → C₃ – C₂, we get

D = `|(10, 57, 50),(12, 64, 60),(15, 78, 75)|`

Taking (5) common from C₃, we get

D = `5|(10, 57, 10),(12, 64, 12),(15, 78, 15)|`

= 5(0)  ...[∵ C₁ and C₃ are identical]

= 0