b. How many vectors are in Span{v1, V2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The number of vectors in Span{v,, v2, V3} is O B. There are infinitely many vectors in Span{v,, v2. V3}. c. Is w in the subspace spanned by {v1. v2. v3}? O A. Vector w is in the subspace spanned by {v1, v2, V3} because the subspace generated by v,, v2, and v3 is R°. O B. Vector w is in the subspace spanned by {v1, v2, V3} because w is a linear combination of v1, V2, and v3, which can be seen because any echelon form of the augmented matrix of the system has no row of the form [0 ·.. 0 b] with b# 0. O C. Vector w is not in the subspace spanned by {v1, V2, V3} because w is not a linear combination of v1, v2, and v3. O D. Vector w is not in the subspace spanned by {v1. V2. V3} because the rightmost column of the augmented matrix of the system x, v, +X2V2 + X3V3 = w is a pivot column.
b. How many vectors are in Span{v1, V2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The number of vectors in Span{v,, v2, V3} is O B. There are infinitely many vectors in Span{v,, v2. V3}. c. Is w in the subspace spanned by {v1. v2. v3}? O A. Vector w is in the subspace spanned by {v1, v2, V3} because the subspace generated by v,, v2, and v3 is R°. O B. Vector w is in the subspace spanned by {v1, v2, V3} because w is a linear combination of v1, V2, and v3, which can be seen because any echelon form of the augmented matrix of the system has no row of the form [0 ·.. 0 b] with b# 0. O C. Vector w is not in the subspace spanned by {v1, V2, V3} because w is not a linear combination of v1, v2, and v3. O D. Vector w is not in the subspace spanned by {v1. V2. V3} because the rightmost column of the augmented matrix of the system x, v, +X2V2 + X3V3 = w is a pivot column.
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
![b. How many vectors are in Span{v1, v2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The number of vectors in Span{v,, v2. V3} is
O B. There are infinitely many vectors in Span{v,, v2. V3}.
c. Is w in the subspace spanned by {v,, V2, V3}?
O A. Vector w is in the subspace spanned by {v,, v2, V3} because the subspace generated by v1, v2, and v3 is R°.
O B. Vector w is in the subspace spanned by {v1, V2, V3} because w is a linear combination of v1, V2, and v3, which can be seen because any echelon form
of the augmented matrix of the system has no row of the form [0 •.. 0 b] with b+ 0.
O C. Vector w is not in the subspace spanned by {v1, V2, V3} because w is not a linear combination of v1, v2, and v3.
O D. Vector w is not in the subspace spanned by {v1, v2, V3} because the rightmost column of the augmented matrix of the system x, v, + xX2V2 + X3V3 = w is
a pivot column.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33d1b54b-5ad7-47f0-bdad-cbb23fbe6ef6%2Fd9e104cb-53ae-405f-adef-659f2eb65e8b%2Faioarpd_processed.png&w=3840&q=75)
Transcribed Image Text:b. How many vectors are in Span{v1, v2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The number of vectors in Span{v,, v2. V3} is
O B. There are infinitely many vectors in Span{v,, v2. V3}.
c. Is w in the subspace spanned by {v,, V2, V3}?
O A. Vector w is in the subspace spanned by {v,, v2, V3} because the subspace generated by v1, v2, and v3 is R°.
O B. Vector w is in the subspace spanned by {v1, V2, V3} because w is a linear combination of v1, V2, and v3, which can be seen because any echelon form
of the augmented matrix of the system has no row of the form [0 •.. 0 b] with b+ 0.
O C. Vector w is not in the subspace spanned by {v1, V2, V3} because w is not a linear combination of v1, v2, and v3.
O D. Vector w is not in the subspace spanned by {v1, v2, V3} because the rightmost column of the augmented matrix of the system x, v, + xX2V2 + X3V3 = w is
a pivot column.
Transcribed Image Text:1
2
7
Let v, =
and w =
- 1
3
8
2
a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2. V3}?
b. How many vectors are in Span{v1, V2, V3}?
c. Is w in the subspace spanned by {v1, V2, V3}? Why?
a. Is w in {v1, V2. V3}?
O A. Vector w is not in {v1, v2, V3} because it is not v1, V2, or v3.
O B. Vector w is in {v1, v2, V3} because it is a linear combination of v,, v2, and v3.
O C. Vector w is not in {v1, v2, V3} because it is not a linear combination of v1, V2, and v3.
O D. Vector w is in {v1, V2, V3} because the subspace generated by v1, V2, and v3 is R°.
How many vectors are in {v1, v2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The number of vectors in {v1, V2, V3} is
O B. There are infinitely many vectors in {v1, V2, V3).
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