Let v₁ = 4 1, V3 = 5 Choose the correct answer below. 12 3 15 and w= 1 6 Is w in the subspace spanned by {V₁, V₂, V3}? Why? 11 O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³. 11 O B. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation X₁ V₁ +X₂V₂ +X3V3 = w has no solution which can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b 0. 11 OC. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁V₁ + X₂V₂ + X3 V3 =W is not a pivot column. O D. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3- 1
Let v₁ = 4 1, V3 = 5 Choose the correct answer below. 12 3 15 and w= 1 6 Is w in the subspace spanned by {V₁, V₂, V3}? Why? 11 O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³. 11 O B. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation X₁ V₁ +X₂V₂ +X3V3 = w has no solution which can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b 0. 11 OC. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁V₁ + X₂V₂ + X3 V3 =W is not a pivot column. O D. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3- 1
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
![4
12
9000
V3 =
5
15
Let V₁ =
1
-1
V₂=
5
and w= 1 Is w in the subspace spanned by {V₁, V₂, V3}? Why?
6
Choose the correct answer below.
O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
11
1:
B. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation X₁ V₁ +X₂V₂ + X3 V3 = w has no solution which
can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b *0.
O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system
X₁V₁ + X₂V₂ + X₂ V3 = w is not a pivot column.
O D. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3-
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F982437f2-81fd-4f07-8f8a-fea4c039ac1e%2F4bf0cb7f-8bc7-40fb-8441-9020d3b187b8%2Fobpste9_processed.png&w=3840&q=75)
Transcribed Image Text:4
12
9000
V3 =
5
15
Let V₁ =
1
-1
V₂=
5
and w= 1 Is w in the subspace spanned by {V₁, V₂, V3}? Why?
6
Choose the correct answer below.
O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
11
1:
B. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation X₁ V₁ +X₂V₂ + X3 V3 = w has no solution which
can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b *0.
O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system
X₁V₁ + X₂V₂ + X₂ V3 = w is not a pivot column.
O D. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3-
11
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