Find k, if A= [(3, -2),(4, -2)] and if A2 = kA – 2I

Questions

Find k, if A= `[(3, -2),(4, -2)]` and if A² = kA – 2I

If A = `[(3, -2),(4, -2)], I = [(1, 0),(0, 1)]` and A² = kA − 2I, find the value of k.

Sum

Solution

A² = kA – 2I

∴ A·A + 2I = kA

∴ `[(3, -2),(4, -2)] [(3, -2),(4, -2)] + 2[(1, 0),(0, 1)] = "k"[(3, -2),(4, -2)]`

∴ `[(9 - 8, -6 + 4),(12 - 8, -8 + 4)] + [(2, 0),(0, 2)] = [(3"k", -2"k"),(4"k", -2"k")]`

∴ `[(1, -2),(4, -4)] + [(2, 0),(0, 2)] = [(3"k", -2"k"),(4"k", -2"k")]`

∴ `[(3, -2),(4, -2)] = [(3"k", -2"k"),(4"k", -2"k")]`

∴ By equality of matrices, we get

3k = 3

∴ k = 1

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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 19 | Page 95

Nootan Mathematics [English] Class 10 ICSE

Chapter 8 Matrices
Exercise 8C | Q 26. | Page 165

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