22. Determine the values of a such that the matrices
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
Help with question 22
![In Exercises 15-18, explain, without solving a linear
system, why the set of vectors is linearly dependent.
15. V₁ =
16. V₁ =
V3
17. V₁ =
V3 =
18. V₁ =
V3 =
4
-A
2
[ - ] v² = [2¹²]
V2
[3]
19. a. A =
-1
4
b. A =
20. a. A =
-6
b. A =
2
V₂ =
In Exercises 19 and 20, explain, without solving a
linear system, why the column vectors of the matrix A
are linearly dependent.
[ 32]
-2
-1
V₂ =
-1
2 5
-6 3
3
2 -4 3
V2 =
2 1 3
1
2
−1
3
4 −1
5 -2
[8]
0
310
1 0
20
2 3
3 1
-1 0
5 2
629
4 -3 -2
21. Determine the values of a such that the vectors
[] []
are linearly independent.
2.3 Linear Independence 121
22. Determine the values of a such that the matrices
2
619
²]
]
23. Let
are linearly independent.
0
--0--0
V2 = 2
=
24. Let
can be written as
a. Show that the vectors are linearly independent.
b. Find the unique scalars c₁, C2, C3 such that the
vector
V =
3
1
M-[48] -
M₁
=
M₂ =
-1
M-88
M3
1
2
a
V = C₁V1 + C2V2 + C3V3
–4
[3]
-2
M =
can be written as
--0
V3 =
2
a. Show that the matrices are linearly
independent.
3 5
4
3
b. Find the unique scalars c₁, C2, C3 such that the
matrix
08
M = C₁ M₁ + C2M2 + C3 M3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8783cbc5-0f10-43ba-8bd7-4625ee264f91%2F8d73dc7c-d809-4eb8-92f9-cd3e44b15cef%2Fwzk7jyk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 15-18, explain, without solving a linear
system, why the set of vectors is linearly dependent.
15. V₁ =
16. V₁ =
V3
17. V₁ =
V3 =
18. V₁ =
V3 =
4
-A
2
[ - ] v² = [2¹²]
V2
[3]
19. a. A =
-1
4
b. A =
20. a. A =
-6
b. A =
2
V₂ =
In Exercises 19 and 20, explain, without solving a
linear system, why the column vectors of the matrix A
are linearly dependent.
[ 32]
-2
-1
V₂ =
-1
2 5
-6 3
3
2 -4 3
V2 =
2 1 3
1
2
−1
3
4 −1
5 -2
[8]
0
310
1 0
20
2 3
3 1
-1 0
5 2
629
4 -3 -2
21. Determine the values of a such that the vectors
[] []
are linearly independent.
2.3 Linear Independence 121
22. Determine the values of a such that the matrices
2
619
²]
]
23. Let
are linearly independent.
0
--0--0
V2 = 2
=
24. Let
can be written as
a. Show that the vectors are linearly independent.
b. Find the unique scalars c₁, C2, C3 such that the
vector
V =
3
1
M-[48] -
M₁
=
M₂ =
-1
M-88
M3
1
2
a
V = C₁V1 + C2V2 + C3V3
–4
[3]
-2
M =
can be written as
--0
V3 =
2
a. Show that the matrices are linearly
independent.
3 5
4
3
b. Find the unique scalars c₁, C2, C3 such that the
matrix
08
M = C₁ M₁ + C2M2 + C3 M3
Expert Solution
Step 1
22. Given that the matrices are
Step by step
Solved in 2 steps
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