a) Give an example of two matrices A, B € M3,3 (C) such that det (A + B) # det A+ det B. b) Is it true that the map det : M3.3 (C) → C is linear?
a) Give an example of two matrices A, B € M3,3 (C) such that det (A + B) # det A+ det B. b) Is it true that the map det : M3.3 (C) → C is linear?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 52EQ
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Needed to be solved a and b parts correctly in 15 minutes and get the thumbs up please show neat and clean work
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![a) Give an example of two matrices A, B E M3,3 (C) such that
det A + det B.
det (A + B)
b) Is it true that the map det: M3,3 (C) → C is linear?
SCHOOL OF MATHEMATICS AND STATISTICS
Maple Output:
> with (Linear Algebra):
> Q, R QRDecomposition (<< 1, 2, 1, -1><0, -6, -5, 4>>);
> Q. Transpose (Q);
[1/2
[7]
[----
> IdentityMatrix (4) Q. Transpose(Q);
[ 7
[
[
[27
Q. R [
1/2
[7]
[1/2
[7]
[----
[7
[
[1/2
[7]
(- ----
[7
Page 1 of 2
[11]
[ --
[14]
[
[2/7
[
[-2/7
[
[1/14
1/2]
3 14 ]
2/7
------]
4/7
14
7]
]
1/2 ]
14 ]
-----]
14 1
]
]
1
]
0]
] [7
], [
1/2] [
14 ] [ 0
[3/14 -2/7
[
[
-2/7
2/7
2/7 3/7
-2/7 -2/7
[1/2
[-2/7 3/7 -2/7
[
[2/7
4/7
[
[-1
[14]
-2/7 1/14]
2/7
2/7 -2/7]
BIELSUSLEIE UŠUŠLE
2/7
1/2]
-37 1
14 ]
UNIVERSITY OF NEW SOUTH WALES
1/2 ]
14 ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd580b721-3664-446f-9ceb-e2cc456c38cd%2Ff9ec7f5d-a8d1-4916-9d47-fd4ac624355c%2Fg2itqjq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Give an example of two matrices A, B E M3,3 (C) such that
det A + det B.
det (A + B)
b) Is it true that the map det: M3,3 (C) → C is linear?
SCHOOL OF MATHEMATICS AND STATISTICS
Maple Output:
> with (Linear Algebra):
> Q, R QRDecomposition (<< 1, 2, 1, -1><0, -6, -5, 4>>);
> Q. Transpose (Q);
[1/2
[7]
[----
> IdentityMatrix (4) Q. Transpose(Q);
[ 7
[
[
[27
Q. R [
1/2
[7]
[1/2
[7]
[----
[7
[
[1/2
[7]
(- ----
[7
Page 1 of 2
[11]
[ --
[14]
[
[2/7
[
[-2/7
[
[1/14
1/2]
3 14 ]
2/7
------]
4/7
14
7]
]
1/2 ]
14 ]
-----]
14 1
]
]
1
]
0]
] [7
], [
1/2] [
14 ] [ 0
[3/14 -2/7
[
[
-2/7
2/7
2/7 3/7
-2/7 -2/7
[1/2
[-2/7 3/7 -2/7
[
[2/7
4/7
[
[-1
[14]
-2/7 1/14]
2/7
2/7 -2/7]
BIELSUSLEIE UŠUŠLE
2/7
1/2]
-37 1
14 ]
UNIVERSITY OF NEW SOUTH WALES
1/2 ]
14 ]
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