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Question
Solve the following :
If A = `[(3, 1),(1, 5)], "B" = [(1, 2),(5, -2)]`, verify |AB| = |A| |B|.
Solution
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|.
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