(a) Let A be the matrix 2 3 Compute A100 (b) Let B be the matrix Compute B50 You must show all steps for this problem. Simplify your fir matrices, not products of several matrices. (You are allow that form, of course!)
(a) Let A be the matrix 2 3 Compute A100 (b) Let B be the matrix Compute B50 You must show all steps for this problem. Simplify your fir matrices, not products of several matrices. (You are allow that form, of course!)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 77E
Related questions
Question
100%
![Answer
Key
For part (a), a diagonalization of A is
A = PDP-¹ –
-1 1692
1/3 1/3
-2/3-1/3
SO
A100
1
= PD¹00p-1
5100 +2
32(51001) 2.5100+1
5100 1
(Remember that (-1)100 is just 1, so there's no reason to have the expression (-1)100 in the final, simplified
answer). For part (b), a diagonalization of B is
B = PDP-¹ _
FARINA.
-1
SO
1
B50 PD50p-1 _
[2.350 250 251 2.350]
350 - 250 251 - 350
The matrices P and D in your diagonalizations may be different (you may have listed the eigenvalues in the
other order on the diagonal of D, or chosen different scalar multiples for your eigenvectors as the columns
of P), but your final answers must be the same as mine (any differences "cancel out" after multiplying by
P-¹, since changing P changes P-¹ as well).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa923b6f-81dd-482c-8885-6de6bc295751%2Fb0651d90-3601-4665-a879-4ebfea11fb87%2Fdew0pyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Answer
Key
For part (a), a diagonalization of A is
A = PDP-¹ –
-1 1692
1/3 1/3
-2/3-1/3
SO
A100
1
= PD¹00p-1
5100 +2
32(51001) 2.5100+1
5100 1
(Remember that (-1)100 is just 1, so there's no reason to have the expression (-1)100 in the final, simplified
answer). For part (b), a diagonalization of B is
B = PDP-¹ _
FARINA.
-1
SO
1
B50 PD50p-1 _
[2.350 250 251 2.350]
350 - 250 251 - 350
The matrices P and D in your diagonalizations may be different (you may have listed the eigenvalues in the
other order on the diagonal of D, or chosen different scalar multiples for your eigenvectors as the columns
of P), but your final answers must be the same as mine (any differences "cancel out" after multiplying by
P-¹, since changing P changes P-¹ as well).
Transcribed Image Text:2
(a) Let A be the matrix
Compute A100
3
(b) Let B be the matrix
Compute B50
50 in
You must show all steps for this problem. Simplify your final answers; these answers should be single 2 × 2
matrices, not products of several matrices. (You are allowed to leave numbers of the form n100 or n
that form, of course!)
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