-3 15. (7A)-¹ = 1 -2 -1 17. (1+2A)-¹ = [13] (I 4 5

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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1.4 Questions 15,17 on paper please. They R under 1 Question
(e² - e²^x) (e²+ e^^) ]
—
10. Find the inverse of
cos
sin e
sin e
COS
In Exercises 11-14, verify that the equations are valid for the mat
ces in Exercises 5-8.
11. (AT)-¹ = (A-1)T
1
12. (A-¹)-¹ = A
13. (ABC)-¹ = C-¹B-¹A-¹
14. (ABC) = CTBTAT
In Exercises 15-18, use the given information to find A.
3
15. (7A) ¹:
(16. (5A¹)-¹
=
-
21
17. (I + 2A)-¹
Jem 18. A-¹ =
-
4
5] His
In Exercises 19-20, compute the following using the given matr
a. A³
b. A-3
c. A² - 2A + I
-
20. A
19. A =
In Exercises 21-22, compute p(A) for the given matrix A ar
following polynomials.
a. p(x) = x-2
2²
=
r+1
Transcribed Image Text:(e² - e²^x) (e²+ e^^) ] — 10. Find the inverse of cos sin e sin e COS In Exercises 11-14, verify that the equations are valid for the mat ces in Exercises 5-8. 11. (AT)-¹ = (A-1)T 1 12. (A-¹)-¹ = A 13. (ABC)-¹ = C-¹B-¹A-¹ 14. (ABC) = CTBTAT In Exercises 15-18, use the given information to find A. 3 15. (7A) ¹: (16. (5A¹)-¹ = - 21 17. (I + 2A)-¹ Jem 18. A-¹ = - 4 5] His In Exercises 19-20, compute the following using the given matr a. A³ b. A-3 c. A² - 2A + I - 20. A 19. A = In Exercises 21-22, compute p(A) for the given matrix A ar following polynomials. a. p(x) = x-2 2² = r+1
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