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Question
Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)] "A" = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`
Solution
Order of matrix `[(2, -1),(1, 0),(-3, 4)]` is 3 × 2 and the matrix
`[(-1, -8, -10),(1, -2, -5),(9, 22, 15)]` is 3 × 3
∴ Order of matrix A must be 2 × 3
Let A = `[("a", "b", "c"),("d", "e", "f")]_(2 xx 3)`
So, `[(2, -1),(1, 0),(-3, 4)] [("a", "b", "c"),("d", "e", "f")] = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`
`[(2"a" - "d", 2"b" - "e", 2"c" - "f"),("a" + 0, "b" + 0, "c" + 0),(-3"a" + 4"d", -3"b" + 4"e", -3"c" + 4"f")] = [(-1, -8, -10),(1, -2, -5),(9, 22, 5)]`
Equating the corresponding elements, we get,
2a – d = – 1 and a = 1
⇒ 2 × 1 – d = – 1
⇒ d = 2 + 1
⇒ d = 3
2b – e = – 8 and b = – 2
⇒ 2(– 2) – e
⇒ – 8
⇒ – 4 – e = – 8
⇒ e = 4
2c – f = – 10 and c = – 5
⇒ 2(– 5) – f = – 10
⇒ – 10 – f = – 10
⇒ f = 0
a = 1, b = – 2, c = – 5, d = 3, e = 4 and f = 0
Hence, A = `[(1, -2, -5),(3, 4, 0)]`.
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