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Question
Given `[(2, 1),(-3,4)]` . X = `[(7),(6)]`. Write:
- the order of the matrix X.
- the matrix X.
Solution
Given `[(2,1),(-3,4)]` X = `[(7),(6)]`
i. Let the order of X be a × b
∴ `[(2, 1),(-3, 4)]_(2 xx 2) . X_(a xx b) = [(7),(6)]_(2 xx 1)`
`=>` a = 2 and b = 1
∴ The order of the matrix X = a × b = 2 × 1
ii. Let `X = [(x),(y)]`
∴ `[(2, 1),(-3, 4)][(x),(y)] = [(7),(6)]`
`=> [(2x + y),(-3x + 4y)] = [(7),(6)]`
2x + y = 7 ...(1)
–3x + 4y = 6 ...(2)
Multiplying (1) by 4 and subtracting from (2)
`=>` –11x = –22
`=> x = (-22)/(-11) = 2`
Form (1),
y = 7 – 2x
= 7 – 2(2)
= 7 – 4
= 3
∴ The matrix `X = [(x),(y)] = [(2),(3)]`
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