2. Find all vectors [10] [8]. so that the following vector equation can be solved for c₁ and c₂: [T] C1 +8-8 + C₂ =
2. Find all vectors [10] [8]. so that the following vector equation can be solved for c₁ and c₂: [T] C1 +8-8 + C₂ =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Help with question #2
![Please show all applicable work. Be sure to write your work and answers clearly and neatly.
Use your own paper. Please submit this exam using pdf format of Syllabus
I
1. Using the vectors u =
2. Find all vectors
3]
0
10
M
and v=
[8]
, so that the following vector equation can be solved for c₁ and c₂:
C1
2
C1
1
[3]
3. Determine the values of a such that the vectors
5. Consider the matrix A =
36
10 find u + 5v.
π
and M₁ =
1
2
1
+ C2
are linearly independent.
4. Determine if the matrix M is a linear combination of the matrices M₁, M₂ and M3:
2 3
-1 1
1 2
1 2
3
1
2
a
[B]-[8]
6
2
·A·B
1
4
2 2
1
SA
2, M₂ = [
1
2 1
and the vector b
If so, determine scalars C₁, C2, C3 such that c₁ M₁ + C₂M₂+ C3 M3
5
3
[124]
[³]
5
>
=
M3
=
a) Compute the vector Ab.
b) Let A₁ be the first column of A, A₂ be the second column of A. Compute 3A₁+5A2.
c) How do the answers from (a) and (b) compare? explain.
6. Let S be a finite set of distinct nonzero vectors in R¹2, and |S|=the number of vectors in
the set S. If |S| = 14, are the vectors in S linearly independent or linearly dependent?
Explain.
7. Assume vectors V₁, V2, V3 are nonzero. Explain why the set S = {V1, V2, V3} is linearly
dependent if v3 = 2v1 + 3v2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8783cbc5-0f10-43ba-8bd7-4625ee264f91%2Facfbb062-bf7a-4daa-b1d1-a9e2f1a6fa49%2F6l017np_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please show all applicable work. Be sure to write your work and answers clearly and neatly.
Use your own paper. Please submit this exam using pdf format of Syllabus
I
1. Using the vectors u =
2. Find all vectors
3]
0
10
M
and v=
[8]
, so that the following vector equation can be solved for c₁ and c₂:
C1
2
C1
1
[3]
3. Determine the values of a such that the vectors
5. Consider the matrix A =
36
10 find u + 5v.
π
and M₁ =
1
2
1
+ C2
are linearly independent.
4. Determine if the matrix M is a linear combination of the matrices M₁, M₂ and M3:
2 3
-1 1
1 2
1 2
3
1
2
a
[B]-[8]
6
2
·A·B
1
4
2 2
1
SA
2, M₂ = [
1
2 1
and the vector b
If so, determine scalars C₁, C2, C3 such that c₁ M₁ + C₂M₂+ C3 M3
5
3
[124]
[³]
5
>
=
M3
=
a) Compute the vector Ab.
b) Let A₁ be the first column of A, A₂ be the second column of A. Compute 3A₁+5A2.
c) How do the answers from (a) and (b) compare? explain.
6. Let S be a finite set of distinct nonzero vectors in R¹2, and |S|=the number of vectors in
the set S. If |S| = 14, are the vectors in S linearly independent or linearly dependent?
Explain.
7. Assume vectors V₁, V2, V3 are nonzero. Explain why the set S = {V1, V2, V3} is linearly
dependent if v3 = 2v1 + 3v2.
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