Problem 4 Let V be the span of the following vectors F 3 V1 = U2 = -2 2 V3 = 8 6 U4 = V5 = V6 = -1 5 1. Why these six vectors are NOT linearly independent? Explain? 2. Find a basis for V = span{v1, U2, U3, U4: U5, U6). 3. What is the dimension of V? Why? The following vector is in V, write it as a linear combination of the basis vectors you found in part (2). u= [2 2 2 10]"
Problem 4 Let V be the span of the following vectors F 3 V1 = U2 = -2 2 V3 = 8 6 U4 = V5 = V6 = -1 5 1. Why these six vectors are NOT linearly independent? Explain? 2. Find a basis for V = span{v1, U2, U3, U4: U5, U6). 3. What is the dimension of V? Why? The following vector is in V, write it as a linear combination of the basis vectors you found in part (2). u= [2 2 2 10]"
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
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Question
Base of a vector space
![Problem 4 Let V be the span of the following vectors
61
3
=
Solution 4:
U₂ =
1
2
V3 =
8
6
U4 =
1
V5 =
400
u= [2 2 2 10]"
0
6
2
lo
bertaz
1. Why these six vectors are NOT linearly independent? Explain?
2. Find a basis for V = span{v1, U2, U3, U4: U5, V6).
3. What is the dimension of V? Why? The following vector is in V, write it as a linear combination
of the basis vectors you found in part (2).
V6 =
7
od 02](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe52e616-7bd7-4d85-a476-7e5fcec53ee5%2Fbe0042f1-604c-4700-8f40-26cde41056e5%2Fxgdmre6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 4 Let V be the span of the following vectors
61
3
=
Solution 4:
U₂ =
1
2
V3 =
8
6
U4 =
1
V5 =
400
u= [2 2 2 10]"
0
6
2
lo
bertaz
1. Why these six vectors are NOT linearly independent? Explain?
2. Find a basis for V = span{v1, U2, U3, U4: U5, V6).
3. What is the dimension of V? Why? The following vector is in V, write it as a linear combination
of the basis vectors you found in part (2).
V6 =
7
od 02
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