Question

Solve the following :

If A = `[(3, 1),(1, 5)], "B" = [(1, 2),(5, -2)]`, verify |AB| = |A| |B|.

Answer 1

AB = `[(3, 1),(1, 5)][(1, 2),(5, -2)]`

= `[(3 + 5, 6 - 2),(1 + 25, 2 - 10)]`

= `[(8, 4),(26, -8)]`

∴ |AB| = `|(8, 4),(26, -8)|`

= – 64 – 104
= – 168

|A| = `|(3, 1),(1, 5)|`

= 15 – 1
= 14

|B| = `|(1, 2),(5, -2)|`

= 2 – 10
= – 12
∴ |A| · |B| = 14(– 12) = – 168
∴ |AB| = |A| · |B|.