Let V₁ = 1 -1 3 4 Choose the correct answer below. 11 10 and w= 4 1 9 Is w in the subspace spanned by {V₁. V₂, V3}? Why? O A. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation x₁ V₁ +X₂V₂ + X₂ 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. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3- 11 1 O B. O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + X₂V₂ + X₂ V3 =W is not a pivot column. D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
Let V₁ = 1 -1 3 4 Choose the correct answer below. 11 10 and w= 4 1 9 Is w in the subspace spanned by {V₁. V₂, V3}? Why? O A. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation x₁ V₁ +X₂V₂ + X₂ 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. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3- 11 1 O B. O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + X₂V₂ + X₂ V3 =W is not a pivot column. D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
Related questions
Question
![Let V₁ =
1
-1
3
4
Choose the correct answer below.
11
10
and w=
4
1
9
Is w in the subspace spanned by {V₁.
V₂, V3}? Why?
O A. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation x₁ V₁ +X₂V₂ + X₂ 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.
Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3-
11
1
O B.
O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system
X₁ V₁ + X₂V₂ + X₂ V3 =W is not a pivot column.
D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F982437f2-81fd-4f07-8f8a-fea4c039ac1e%2F732ea59e-5452-4a8d-9459-e6a260556015%2Fha3y9x_processed.png&w=3840&q=75)
Transcribed Image Text:Let V₁ =
1
-1
3
4
Choose the correct answer below.
11
10
and w=
4
1
9
Is w in the subspace spanned by {V₁.
V₂, V3}? Why?
O A. Vector w is not in the subspace spanned by {V₁, V₂, V3} because the equation x₁ V₁ +X₂V₂ + X₂ 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.
Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3-
11
1
O B.
O C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system
X₁ V₁ + X₂V₂ + X₂ V3 =W is not a pivot column.
D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
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