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(a) The matrix M is given by M = 2 (1) (11) (111) (iv) (v) 00 1 -1 0/ Evaluate M-¹ (using elementary row operations). Evaluate M². Use Matrix M to show that M² + 6M-1 = 71 where I is the 3 x 3 identity matrix and 0 is the zero matrix of the same order. Use the result in (ii) to show that M³ = 7M - 61. Find M³. (b) Find all the values of such that matrix B is a singular matrix. 1 λ λ 8-(10) B = 1 3 9

(a) The matrix M is given by M = 2 (1) (11) (111) (iv) (v) 00 1 -1 0/ Evaluate M-¹ (using elementary row operations). Evaluate M². Use Matrix M to show that M² + 6M-1 = 71 where I is the 3 x 3 identity matrix and 0 is the zero matrix of the same order. Use the result in (ii) to show that M³ = 7M - 61. Find M³. (b) Find all the values of such that matrix B is a singular matrix. 1 λ λ 8-(10) B = 1 3 9

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...
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'0 (a) The matrix M is given by M = 2 1 -1 0, Evaluate M-¹ (using elementary row operations). Evaluate M². (11) (111) 2 3 0 0 (iv) (v) Use Matrix M to show that M² + 6M-1 = 71 where I is the 3 x 3 identity matrix and 0 is the zero matrix of the same order. Use the result in (11) to show that M³ = 7M - 61. Find M³ (b) Find all the values of such that matrix B is a singular matrix. (1 λ λ2) 1 1 3 9 B = 1 \1
Transcribed Image Text:'0 (a) The matrix M is given by M = 2 1 -1 0, Evaluate M-¹ (using elementary row operations). Evaluate M². (11) (111) 2 3 0 0 (iv) (v) Use Matrix M to show that M² + 6M-1 = 71 where I is the 3 x 3 identity matrix and 0 is the zero matrix of the same order. Use the result in (11) to show that M³ = 7M - 61. Find M³ (b) Find all the values of such that matrix B is a singular matrix. (1 λ λ2) 1 1 3 9 B = 1 \1
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