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Question
Given `[(2, 1),(-3, 4)] x = [(7),(6)]` Write the matrix x.
Solution
Let `x = [(x),(y)]`
∴ `[(2, 1),(-3, 4)] xx [(x),(y)] = [(7),(6)]`
⇒ `[(2x + y),(-3x + 4y)] = [(7),(6)]`
⇒ 2x + y = 7 ...(1)
-3x + 4y = 6 ...(2)
Multiplying by 4 in equation (1) and solving with equation (2)
8x + 4y = 28
-3x + 4y = 6
(+) (-) (-)
11x = 22
x = 2
Putting the value of x in equation (1), we get
∴ 2 × 2 + y = 7
y = 7 - 4 = 3
∴ The matrix x = `[(x), (y)] = [(2),(3)]`
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