4 k V1 = V2 = -5 ; y= -6 -2 k For what value(s) of k is y in the plane spanned by vị and v2?
4 k V1 = V2 = -5 ; y= -6 -2 k For what value(s) of k is y in the plane spanned by vị and v2?
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
![### Problem Statement:
Given the vectors:
\[
\mathbf{v}_1 = \begin{pmatrix} 3 \\ 1 \\ 5 \end{pmatrix}; \quad \mathbf{v}_2 = \begin{pmatrix} -2 \\ -5 \\ 1 \end{pmatrix}; \quad \mathbf{y} = \begin{pmatrix} 4k \\ -6 \\ -2k \end{pmatrix}
\]
The question asks: For what value(s) of \( k \) is \(\mathbf{y}\) in the plane spanned by \(\mathbf{v}_1\) and \(\mathbf{v}_2\)?
Instructions:
- Show all your work, do not skip steps.
- Displaying only the final answer is not enough to get credit.
This problem requires you to determine the value(s) of \( k \) such that the vector \(\mathbf{y}\) can be expressed as a linear combination of the vectors \(\mathbf{v}_1\) and \(\mathbf{v}_2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf0a178e-b4ea-4552-8c3f-e1ff6984e724%2F9c021661-d71b-4685-bd5e-17314b9eebf3%2Funm95zc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Given the vectors:
\[
\mathbf{v}_1 = \begin{pmatrix} 3 \\ 1 \\ 5 \end{pmatrix}; \quad \mathbf{v}_2 = \begin{pmatrix} -2 \\ -5 \\ 1 \end{pmatrix}; \quad \mathbf{y} = \begin{pmatrix} 4k \\ -6 \\ -2k \end{pmatrix}
\]
The question asks: For what value(s) of \( k \) is \(\mathbf{y}\) in the plane spanned by \(\mathbf{v}_1\) and \(\mathbf{v}_2\)?
Instructions:
- Show all your work, do not skip steps.
- Displaying only the final answer is not enough to get credit.
This problem requires you to determine the value(s) of \( k \) such that the vector \(\mathbf{y}\) can be expressed as a linear combination of the vectors \(\mathbf{v}_1\) and \(\mathbf{v}_2\).
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