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Question
If A = `[(3 , 1),(-1 , 2)]` and B =`[(7),(0)]`, find matrix C if AC = B.
Solution
Let C = `[(a),(b)]` then
AC = B
⇒ `[(3 , 1),(-1 , 2)][(a),(b)] = [(7),(0)]`
⇒ `[(3a + b),(-a + 2b)] = [(7),(0)]`
⇒ 3a + b = 7 ...(1)
- a + 2b = 0 ...(2)
From equation (1),
6a + 2b = 14 ...(3)
From (3) - (2) given
7a = 14
⇒ a = 2
Put a = 2 in (1), we get
6 + b = 7
⇒ b = 7 - 6 = 1
∴ C = `[(2),(1)]`.
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