Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers. 1. 5 -3 7 -6 2. -4 ;] 6-9
Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers. 1. 5 -3 7 -6 2. -4 ;] 6-9
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
1
![R
5 ZETO
Canide
27200.1
33. A¹ = B =
35.
-6
4
0
0
j = 1,...,n, let a, b,, and e, denote the j th columns of
A, B, and I, respectively. Use the facts that a, - aj+1 =
and bj = ej-ej+1 for j = 1,...,n - 1, and
ej
a = b = en.
1 1
-1
0
Find this by row reducing [A
37. C =
3]
39. 27,.30, and .23 inch, respectively
41. [M] 12, 1.5,21.5, and 12 newtons, respectively
0
:
0
3
0
0
Section 2.3, page 117
The abbreviation IMT (here and in the Study Guide) denotes the
Invertible Matrix Theorem (Theorem 8).
e3 ].
1. Invertible, by the IMT. Neither column of the matrix is a
multiple of the other column, so they are linearly
independent. Also, the matrix is invertible by Theorem 4 in
Section 2.2 because the determinant is nonzero.
3. Invertible, by the IMT. The matrix row reduces to
5
0
-7
Hint: For
0 -1
0
5. Not invertible, by the IMT. The matrix row reduces to
2
-5
0
0
0 and has 3 pivot positions.
and is not row equivalent to 13.
17. If A is
By (e)
linearly
19. By (e)
Dx =
Can yo
21. The ma
2.2 or
02
IMT is
span R
23. Statem
and (h
depene
25. Hint: U
27. Let W
A(BW
not pra
before
29. Since t
statem
the tra
A is no
XA
31. Hint: L
A has
Could
33. Hint: E
Then L
T-(x
35. Hint: T
T(u) =
that u
an arbi](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcee71cba-b5b8-44a0-9e00-7f1c17b6ad3a%2Fdb0f8062-b3c0-43b4-9121-f55983d8203f%2Frgi7vk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:R
5 ZETO
Canide
27200.1
33. A¹ = B =
35.
-6
4
0
0
j = 1,...,n, let a, b,, and e, denote the j th columns of
A, B, and I, respectively. Use the facts that a, - aj+1 =
and bj = ej-ej+1 for j = 1,...,n - 1, and
ej
a = b = en.
1 1
-1
0
Find this by row reducing [A
37. C =
3]
39. 27,.30, and .23 inch, respectively
41. [M] 12, 1.5,21.5, and 12 newtons, respectively
0
:
0
3
0
0
Section 2.3, page 117
The abbreviation IMT (here and in the Study Guide) denotes the
Invertible Matrix Theorem (Theorem 8).
e3 ].
1. Invertible, by the IMT. Neither column of the matrix is a
multiple of the other column, so they are linearly
independent. Also, the matrix is invertible by Theorem 4 in
Section 2.2 because the determinant is nonzero.
3. Invertible, by the IMT. The matrix row reduces to
5
0
-7
Hint: For
0 -1
0
5. Not invertible, by the IMT. The matrix row reduces to
2
-5
0
0
0 and has 3 pivot positions.
and is not row equivalent to 13.
17. If A is
By (e)
linearly
19. By (e)
Dx =
Can yo
21. The ma
2.2 or
02
IMT is
span R
23. Statem
and (h
depene
25. Hint: U
27. Let W
A(BW
not pra
before
29. Since t
statem
the tra
A is no
XA
31. Hint: L
A has
Could
33. Hint: E
Then L
T-(x
35. Hint: T
T(u) =
that u
an arbi
![for
the
ing
o is in
s A is
linear
■
from
(by
and
2.3 EXERCISES
Unless otherwise specified, assume that all matrices in these
exercises are nxn. Determine which of the matrices in Exercises
1-10 are invertible. Use as few calculations as possible. Justify
your answers.
5
7
1.
·[36
-6
3.
5.
7.
5
0
-3 -7
8
5
0
1
-4
-2
0
1-1 dm-3
35
9. [M]
beo
5
6
0
-9
4
-6
7
-1
10. [M] 7
9
8
3
4
+565
0
-1
527
-6 3 2
-1 2
1
LON
-5 noi
6.
100
2.
4
4.
Ono 1 21 01 1
8-3
8.
0 -7 -7
1
11
-5
10
2
3
3 10
[*]
-7
dan to L
CL
100 7
2 8 -8
9
2 11
9
19
-1
-9-5
0
3 0
2
0
1
0
-3
0
0
om
9.07.
3
5
-5
500
3
6
-1
7
9
2
00
9
-4
4
0
4
In Exercises 11 and 12, the matrices are all nxn. Each part of
the exercises is an implication of the form "If "statement 1",
then "statement 2"." Mark an implication as True if the truth of
"statement 2" always follows whenever "statement 1" happens
to be true. An implication is False if there is an instance in
which "tota
1" is true Iustify each
4680
10
2.3
d. If t
the
e. If
5.59
in
to
13. An m
belox
PASW
14. An
abov
is a
ansv
15. Can
ible
16. Is it
colu
17. If A
ind
18. If C
vi
has
19. If
wh
20. If
th-
21. If
y
22. If
C:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcee71cba-b5b8-44a0-9e00-7f1c17b6ad3a%2Fdb0f8062-b3c0-43b4-9121-f55983d8203f%2Fxdycedb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:for
the
ing
o is in
s A is
linear
■
from
(by
and
2.3 EXERCISES
Unless otherwise specified, assume that all matrices in these
exercises are nxn. Determine which of the matrices in Exercises
1-10 are invertible. Use as few calculations as possible. Justify
your answers.
5
7
1.
·[36
-6
3.
5.
7.
5
0
-3 -7
8
5
0
1
-4
-2
0
1-1 dm-3
35
9. [M]
beo
5
6
0
-9
4
-6
7
-1
10. [M] 7
9
8
3
4
+565
0
-1
527
-6 3 2
-1 2
1
LON
-5 noi
6.
100
2.
4
4.
Ono 1 21 01 1
8-3
8.
0 -7 -7
1
11
-5
10
2
3
3 10
[*]
-7
dan to L
CL
100 7
2 8 -8
9
2 11
9
19
-1
-9-5
0
3 0
2
0
1
0
-3
0
0
om
9.07.
3
5
-5
500
3
6
-1
7
9
2
00
9
-4
4
0
4
In Exercises 11 and 12, the matrices are all nxn. Each part of
the exercises is an implication of the form "If "statement 1",
then "statement 2"." Mark an implication as True if the truth of
"statement 2" always follows whenever "statement 1" happens
to be true. An implication is False if there is an instance in
which "tota
1" is true Iustify each
4680
10
2.3
d. If t
the
e. If
5.59
in
to
13. An m
belox
PASW
14. An
abov
is a
ansv
15. Can
ible
16. Is it
colu
17. If A
ind
18. If C
vi
has
19. If
wh
20. If
th-
21. If
y
22. If
C:
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