Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The image contains a mathematical problem involving vectors. Here's the transcription suitable for an educational website:
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**Problem:**
For what value of \( h \) is \(\vec{y}\) in the plane spanned by \(\vec{v_1}\) and \(\vec{v_2}\)?
- \(\vec{v_1} = \begin{bmatrix} 3 \\ 5 \\ -1 \end{bmatrix}\)
- \(\vec{v_2} = \begin{bmatrix} 9 \\ 13 \\ 1 \end{bmatrix}\)
- \(\vec{y} = \begin{bmatrix} 12 \\ 18 \\ h \end{bmatrix}\)
\( h = \_\_\_\_\_\_\_\)
[Preview Answers] [Submit Answers]
---
**Explanation:**
The problem involves determining the value of \( h \) such that the vector \(\vec{y}\) is within the plane formed by the vectors \(\vec{v_1}\) and \(\vec{v_2}\). This requires the vector \(\vec{y}\) to be a linear combination of \(\vec{v_1}\) and \(\vec{v_2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F233e21da-07a1-46a8-a83f-f0efcb95a6cc%2F03235c2e-6277-4d81-ac2f-7a32eef52a9a%2Fx8dqaak_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical problem involving vectors. Here's the transcription suitable for an educational website:
---
**Problem:**
For what value of \( h \) is \(\vec{y}\) in the plane spanned by \(\vec{v_1}\) and \(\vec{v_2}\)?
- \(\vec{v_1} = \begin{bmatrix} 3 \\ 5 \\ -1 \end{bmatrix}\)
- \(\vec{v_2} = \begin{bmatrix} 9 \\ 13 \\ 1 \end{bmatrix}\)
- \(\vec{y} = \begin{bmatrix} 12 \\ 18 \\ h \end{bmatrix}\)
\( h = \_\_\_\_\_\_\_\)
[Preview Answers] [Submit Answers]
---
**Explanation:**
The problem involves determining the value of \( h \) such that the vector \(\vec{y}\) is within the plane formed by the vectors \(\vec{v_1}\) and \(\vec{v_2}\). This requires the vector \(\vec{y}\) to be a linear combination of \(\vec{v_1}\) and \(\vec{v_2}\).
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