/0 (a) The matrix M is given by M = 2 (1) (11) (111) 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. (b) Find all the values of such that matrix B is a singular matrix. 1 λ λ2) 1 1 1 1 3 9 B =
/0 (a) The matrix M is given by M = 2 (1) (11) (111) 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. (b) Find all the values of such that matrix B is a singular matrix. 1 λ λ2) 1 1 1 1 3 9 B =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please assist and show all working and explanations for all questions
!['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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb72e28a-40cf-4e0b-babe-9ae5dd59d0fc%2F3c4f0e47-88a2-4417-8221-cee23d3d2758%2Fexp5ok8_processed.png&w=3840&q=75)
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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