Consider Sspan 1 -3 5 3 -10 10 What is the dimension of S? -3 10 -10 which is a subspace of R³ Find a basis for S. Enter your answer as a list of vectors separated by commas, and use angle brackets to type each vector, such as '<1,2,3>'. Basis =
Consider Sspan 1 -3 5 3 -10 10 What is the dimension of S? -3 10 -10 which is a subspace of R³ Find a basis for S. Enter your answer as a list of vectors separated by commas, and use angle brackets to type each vector, such as '<1,2,3>'. Basis =
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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![**Problem Statement:**
Consider \( S = \text{span} \left\{ \begin{bmatrix} 1 \\ -3 \\ 5 \end{bmatrix}, \begin{bmatrix} 3 \\ -10 \\ 10 \end{bmatrix}, \begin{bmatrix} -3 \\ 10 \\ -10 \end{bmatrix} \right\} \), which is a subspace of \( \mathbb{R}^3 \).
1. **Find a Basis for \( S \):**
- Enter your answer as a list of vectors separated by commas, and use angle brackets to type each vector, such as \( \langle 1,2,3 \rangle \).
- **Basis =** [Input box provided]
2. **What is the Dimension of \( S \)?**
- **[Input box provided]**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf673b33-84d3-4207-a3d8-77b439e8ab65%2F7b2e87ad-2c4f-4c75-9f7d-845289982780%2Fkhdyyjz_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider \( S = \text{span} \left\{ \begin{bmatrix} 1 \\ -3 \\ 5 \end{bmatrix}, \begin{bmatrix} 3 \\ -10 \\ 10 \end{bmatrix}, \begin{bmatrix} -3 \\ 10 \\ -10 \end{bmatrix} \right\} \), which is a subspace of \( \mathbb{R}^3 \).
1. **Find a Basis for \( S \):**
- Enter your answer as a list of vectors separated by commas, and use angle brackets to type each vector, such as \( \langle 1,2,3 \rangle \).
- **Basis =** [Input box provided]
2. **What is the Dimension of \( S \)?**
- **[Input box provided]**
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