A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A2 = B.

A2 = B &there4; `[(alpha, 0),(1, 1)] [(alpha, 0),(1, 1)] = [(1, 0),(2, 1)]` &there4; `[(alpha^2 + 0, 0 + 0),(alpha + 1, 0 + 1)] = [(1, 0),(2, 1)]` &there4; `[(alpha^2, 0),(alpha + 1, 1)] = [(1, 0),(2, 1)]` &there4; By equality of matrices, we get &there4; α2 = 1 and α + 1 = 2 &there4; α = ± 1 and α = 1 &there4; α = 1

A = [α011],B=[1021] find α, if A2 = B.

Question

A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A² = B.

Sum

Solution

A² = B

∴ `[(alpha, 0),(1, 1)] [(alpha, 0),(1, 1)] = [(1, 0),(2, 1)]`

∴ `[(alpha^2 + 0, 0 + 0),(alpha + 1, 0 + 1)] = [(1, 0),(2, 1)]`

∴ `[(alpha^2, 0),(alpha + 1, 1)] = [(1, 0),(2, 1)]`

∴ By equality of matrices, we get

∴ α² = 1 and α + 1 = 2

∴ α = ± 1 and α = 1

∴ α = 1

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Chapter 4: Determinants and Matrices - Exercise 4.6 [Page 94]

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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 11 | Page 94

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