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

Sum

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

#### 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)]

Concept: Matrices - Properties of Matrix Multiplication
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Exercise 4.6 | Q 18 | Page 95