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Question
If A = `[(2, -1),(-4, 5)] and "B" = [(-3),(2)]` find the matrix C such that AC = B
Solution
Given
A = `[(2, -1),(-4, 5)]`
B = `[(-3),(2)]`
Let martix C = `[(x),(y)]`
∴ AC = `[(2, -1),(-4, 5)][(x),(y)] = [(2x - y),(-4x + 5y)]`
But AC = B
∴ `[(2x - y),(-4x + 5y)] = [(-3),(2)]`
Comparing the corresponding elements
2x – y = –3 ...(i)
–4x + 5y = 2 ...(ii)
Multiplying (i) by 5 and (ii) by 1
10x – 5y = –15
–4x + 5y = 2
Adding, we get
6x = –13
⇒ x = `(-13)/(6)`
Substituting the value of x in (i)
`2((-13)/6) - y` = –3
⇒ `(-13)/(3) - y` = –3
–y = `–3 + (13)/(3)`
= `(-9 + 13)/(3)`
= `(4)/(3)`
∴ y = `-(4)/(3)`
∴ Matrix C = `[((-13)/6),(-4/3)]`.
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