0 (a) The matrix M is given by M = 2 1 -1 0 Evaluate M-¹ (using elementary row operations). Evaluate M². (ii) (iii) 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 (ii) to show that M³ = 7M – 61. Find M³.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer all questions with explantations and working
0
(a) The matrix M is given by M = 2
(i)
(ii)
(iii)
2
3
0
0
1 -1 0
Evaluate M-1 (using elementary row operations).
Evaluate M².
(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 (ii) to show that M³ = 7M - 61.
Find M³.
Transcribed Image Text:0 (a) The matrix M is given by M = 2 (i) (ii) (iii) 2 3 0 0 1 -1 0 Evaluate M-1 (using elementary row operations). Evaluate M². (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 (ii) to show that M³ = 7M - 61. Find M³.
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Hello, could you possibly outline the steps used to solve all parts of steps 3 and 4. I understand the concept behind the question however, I am unable to follow the operations done in each part of the solutions given for the problems solved in steps 3 and step 4. Can you outline each step so I can follow closely thank you. 

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