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प्रश्न
Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`
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उत्तर
Let X = `[("a"),("b")]`
But, AX = B
∴ `[(1, -2),(-2, 1)] [("a"),("b")] = [(-3),(-1)]`
∴ `[("a" - 2"b"),(-2"a" + "b")] = [(-3),(-1)]`
∴ By equality of matrices, we get
a – 2b = – 3 ...(i)
–2a + b = – 1 ...(ii)
By (i) × 2 + (ii), we get
– 3b = – 7
∴ b = `7/3`
Substituting b = `7/3` in (i), we get
`"a" - 2(7/3)` = – 3
∴ a = `- 3 + 14/3 = 5/3`
∴ X = `[(5/3), (7/3)]`
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