Express the indicated vector w as a linear combination of the given vectors v₁ and v₂ if this is possible. If not, show that it is impossible. W = 1 0 0 7 7 8 -6 5 4 -3 6 Select the correct answer below, and fill in the answer box(es) to complete your choice. OA. It is impossible to express the vector w in terms of v₁ and v₂, because an echelon form of the augmented matrix [V₁ V₂ w], E= (Type an integer or simplified fraction for each matrix element.) OB. It is possible to express the vector w in terms of v₁ and v₂, as w= (v₁ + (v₂. (Type integers or fractions.) ,shows that the system is inconsistent.
Express the indicated vector w as a linear combination of the given vectors v₁ and v₂ if this is possible. If not, show that it is impossible. W = 1 0 0 7 7 8 -6 5 4 -3 6 Select the correct answer below, and fill in the answer box(es) to complete your choice. OA. It is impossible to express the vector w in terms of v₁ and v₂, because an echelon form of the augmented matrix [V₁ V₂ w], E= (Type an integer or simplified fraction for each matrix element.) OB. It is possible to express the vector w in terms of v₁ and v₂, as w= (v₁ + (v₂. (Type integers or fractions.) ,shows that the system is inconsistent.
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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Question
![**Express the indicated vector \( w \) as a linear combination of the given vectors \( v_1 \) and \( v_2 \) if this is possible. If not, show that it is impossible.**
\[
w = \begin{bmatrix} 1 \\ 0 \\ 7 \end{bmatrix}, \quad
v_1 = \begin{bmatrix} 7 \\ 8 \\ -6 \end{bmatrix}, \quad
v_2 = \begin{bmatrix} 4 \\ 4 \\ -3 \end{bmatrix}
\]
---
**Select the correct answer below, and fill in the answer box(es) to complete your choice.**
- **A.** It is impossible to express the vector \( w \) in terms of \( v_1 \) and \( v_2 \), because an echelon form of the augmented matrix \( [v_1 \quad v_2 \quad w] \) shows that the system is inconsistent. (Type an integer or simplified fraction for each matrix element.)
\( E = \, \boxed{} \)
- **B.** It is possible to express the vector \( w \) in terms of \( v_1 \) and \( v_2 \), as \( w = (\, \boxed{} \,) v_1 + (\, \boxed{} \,) v_2. \) (Type integers or fractions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a1a8c69-ac20-486b-9f67-8f66504c5494%2Fca6ace37-7566-4630-8d5a-86a7fcfa75ce%2Fpl02ion_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Express the indicated vector \( w \) as a linear combination of the given vectors \( v_1 \) and \( v_2 \) if this is possible. If not, show that it is impossible.**
\[
w = \begin{bmatrix} 1 \\ 0 \\ 7 \end{bmatrix}, \quad
v_1 = \begin{bmatrix} 7 \\ 8 \\ -6 \end{bmatrix}, \quad
v_2 = \begin{bmatrix} 4 \\ 4 \\ -3 \end{bmatrix}
\]
---
**Select the correct answer below, and fill in the answer box(es) to complete your choice.**
- **A.** It is impossible to express the vector \( w \) in terms of \( v_1 \) and \( v_2 \), because an echelon form of the augmented matrix \( [v_1 \quad v_2 \quad w] \) shows that the system is inconsistent. (Type an integer or simplified fraction for each matrix element.)
\( E = \, \boxed{} \)
- **B.** It is possible to express the vector \( w \) in terms of \( v_1 \) and \( v_2 \), as \( w = (\, \boxed{} \,) v_1 + (\, \boxed{} \,) v_2. \) (Type integers or fractions.)
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