Find matrix X such that AX = B, where A = [1-2-21] and B = [-3-1]

Question

Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`

Sum

Solution

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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Q 18 Q 17 Q 19

Chapter 4: Determinants and Matrices - Exercise 4.6 [Page 95]

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Balbharati Mathematics and Statistics (Arts and Science) Part 1 [English] Standard 11 Maharashtra State Board

Chapter 4 Determinants and Matrices
Exercise 4.6 | Q 18 | Page 95

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