Finding the Inverse of a Matrix In Exercises 7-30, find the inverse of the matrix (if it exists). 7. 9. 3. 10. -7 33 11. 12. 4 - 19 13. 3 5 4 14. . 9 3. 6. 5 -7 2 -1 7 - 10 16 -21 10 5 15. 3 16.-5 4 -2 2 3 2 5 17. 3 18. 2 -2 3. 19. 0 3 20. 0.6 21. 0.7 -0.3 0.1 0.2 0.3 -1 0.2 22.-0.3 0.2 0.2 -0.9 0. 0.5 0.5 23. 3 2 24. 3 0 0 2 5 5 4 5 5 2o7 274 200 -- -
Finding the Inverse of a Matrix In Exercises 7-30, find the inverse of the matrix (if it exists). 7. 9. 3. 10. -7 33 11. 12. 4 - 19 13. 3 5 4 14. . 9 3. 6. 5 -7 2 -1 7 - 10 16 -21 10 5 15. 3 16.-5 4 -2 2 3 2 5 17. 3 18. 2 -2 3. 19. 0 3 20. 0.6 21. 0.7 -0.3 0.1 0.2 0.3 -1 0.2 22.-0.3 0.2 0.2 -0.9 0. 0.5 0.5 23. 3 2 24. 3 0 0 2 5 5 4 5 5 2o7 274 200 -- -
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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Done elementary_linear_algebra_8th_..
Z.3 EXercises
2.3
Exercises See CalcChat.com for worked-out solutions to odd-numbered exercises.
The Inverse of a Matrix In Exercises 1-6, show that B
-8
[1
is the inverse of A.
2 0
0 -2
o 0 0 3
8 -7 14
5 -4 6
2 1 -7
-5 10
0 1
1. A- [;
25.
26.
0 0
0 0
B =
-5
1 -2 -1 -2
3 -5 -2
-5 -2
-1
2. A =
B =
4
5
Q 28. 2
-3
@ 27.
3. A =
.2
2
-5
B =
4
4
11
3
6
3
3 -2
4. A =
B =
0 2
4
2
4
6
O 29.
O 30.
3
0 -2
1
3
B =
-2
2
-4
-5
3
2 0
4
5
5. A=
-1
-4
-8
Finding the Inverse of a 2 x 2 Matrix In Exercises
31-36, use the formula on page 66 to find the inverse of
the 2 x 2 matrix (if it exists).
1
4
2 -17 11
2
6. A
-1
11
-7
B=2
4
-3
-
2
3
-2
6.
31.
32.
-1
Finding the Inverse of a Matrix In Exercises 7-30,
find the inverse of the matrix (if it exists).
-4
33.
-6
- 12
34.
2
5
-2
7.
8.
2
3
35.
36.
9.
10.
Finding the Inverse of the Square of a Matrix
In Exercises 37-40, compute A two different ways and
show that the results are equal.
-7
11.
12.
4 - 19
0 -2
3
[-2
2
[1
13. 3
3
2
2
37. A =
-1
38. A =
-5
5
4
14.
3
9.
4]
7 -1
6
5
--
-4
-7
39. A = 0 1
40. A =-2
[1
2 -1
7 - 10
15. 3
7 16 -21
10
5
3
3
2
16.
-5
4
2 -2
Finding the Inverses of Products and Transposes
In Exercises 41-44, use the inverse matrices to find
(a) (AB)-', (b) (AT), and (c) (2A)-.
7
3
2
3
5
17.
3
18.
2
2
4
41. A=
-7
6
B =
.2
-2
3
-4
4
[2
19. 0
42. A--
B-=
3
20.
2
5
1 - -
2
4
[0.6
21. 0.7
-0.3
0.1
0.2
0.3
43. A- = -2
-1
0.2
22.
-0.3
0.2
0.2
-0.9
0.5
0.5
0.5
-4
44. A- =0
4
21
B--2
5
-3
[1
23. 3
2
01
1
24. 3
2
3
4
-1
4
2
4
5
5.
5
Capynge 2T Cmgage Leing AIRgte Reved May the opied ddidwleorin pat. Dcla n d puty ctmy
alew ha demed yped d y ethe al laingpari. Cnga Leing rva eghe e a lo
p. C Lang ade
ng
Chapter 2 Matrices
ng a System of Equations Using an Inverse
ercises 45-48, use an inverse matrix to solve each
n of linear equations.
Singular Matrix In Exercises 55 and 56, find r such
that the matrix is singular.
55. A =|-
56. A -
)x + 2y = -1
46. (a) 2x – y = -3
2r + y = 7
X- 2y =
3
Solving a Matrix Equation In Exercises 57 and 58,
)x+ 2y = 10
x - 2y = -6
(b) 2x - y = -1
find A.
2r + y = -3
2]
a 2
41](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2F76a8307c-5e81-418f-8705-7af7dfd53ca3%2Fw3vzin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1:57
Done elementary_linear_algebra_8th_..
Z.3 EXercises
2.3
Exercises See CalcChat.com for worked-out solutions to odd-numbered exercises.
The Inverse of a Matrix In Exercises 1-6, show that B
-8
[1
is the inverse of A.
2 0
0 -2
o 0 0 3
8 -7 14
5 -4 6
2 1 -7
-5 10
0 1
1. A- [;
25.
26.
0 0
0 0
B =
-5
1 -2 -1 -2
3 -5 -2
-5 -2
-1
2. A =
B =
4
5
Q 28. 2
-3
@ 27.
3. A =
.2
2
-5
B =
4
4
11
3
6
3
3 -2
4. A =
B =
0 2
4
2
4
6
O 29.
O 30.
3
0 -2
1
3
B =
-2
2
-4
-5
3
2 0
4
5
5. A=
-1
-4
-8
Finding the Inverse of a 2 x 2 Matrix In Exercises
31-36, use the formula on page 66 to find the inverse of
the 2 x 2 matrix (if it exists).
1
4
2 -17 11
2
6. A
-1
11
-7
B=2
4
-3
-
2
3
-2
6.
31.
32.
-1
Finding the Inverse of a Matrix In Exercises 7-30,
find the inverse of the matrix (if it exists).
-4
33.
-6
- 12
34.
2
5
-2
7.
8.
2
3
35.
36.
9.
10.
Finding the Inverse of the Square of a Matrix
In Exercises 37-40, compute A two different ways and
show that the results are equal.
-7
11.
12.
4 - 19
0 -2
3
[-2
2
[1
13. 3
3
2
2
37. A =
-1
38. A =
-5
5
4
14.
3
9.
4]
7 -1
6
5
--
-4
-7
39. A = 0 1
40. A =-2
[1
2 -1
7 - 10
15. 3
7 16 -21
10
5
3
3
2
16.
-5
4
2 -2
Finding the Inverses of Products and Transposes
In Exercises 41-44, use the inverse matrices to find
(a) (AB)-', (b) (AT), and (c) (2A)-.
7
3
2
3
5
17.
3
18.
2
2
4
41. A=
-7
6
B =
.2
-2
3
-4
4
[2
19. 0
42. A--
B-=
3
20.
2
5
1 - -
2
4
[0.6
21. 0.7
-0.3
0.1
0.2
0.3
43. A- = -2
-1
0.2
22.
-0.3
0.2
0.2
-0.9
0.5
0.5
0.5
-4
44. A- =0
4
21
B--2
5
-3
[1
23. 3
2
01
1
24. 3
2
3
4
-1
4
2
4
5
5.
5
Capynge 2T Cmgage Leing AIRgte Reved May the opied ddidwleorin pat. Dcla n d puty ctmy
alew ha demed yped d y ethe al laingpari. Cnga Leing rva eghe e a lo
p. C Lang ade
ng
Chapter 2 Matrices
ng a System of Equations Using an Inverse
ercises 45-48, use an inverse matrix to solve each
n of linear equations.
Singular Matrix In Exercises 55 and 56, find r such
that the matrix is singular.
55. A =|-
56. A -
)x + 2y = -1
46. (a) 2x – y = -3
2r + y = 7
X- 2y =
3
Solving a Matrix Equation In Exercises 57 and 58,
)x+ 2y = 10
x - 2y = -6
(b) 2x - y = -1
find A.
2r + y = -3
2]
a 2
41
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