Determine if the set of vectors shown to the right is a basis for R³. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R³. Which of the following describe the set? Select all that apply. A. The set is a basis for R³. B. The set is linearly independent. C. The set spans R³. D. None of the above 3 2 GO -4 1 2 - 9 6 3
Determine if the set of vectors shown to the right is a basis for R³. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R³. Which of the following describe the set? Select all that apply. A. The set is a basis for R³. B. The set is linearly independent. C. The set spans R³. D. None of the above 3 2 GO -4 1 2 - 9 6 3
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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![### Determine Basis and Linear Independence
Determine if the set of vectors shown to the right is a basis for \(\mathbb{R}^3\). If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans \(\mathbb{R}^3\).
\[
\left\{
\begin{bmatrix}
3 \\
-1 \\
1
\end{bmatrix},
\begin{bmatrix}
2 \\
-4 \\
2
\end{bmatrix},
\begin{bmatrix}
-9 \\
6 \\
3
\end{bmatrix}
\right\}
\]
---
### Multiple Choice Question
Which of the following describe the set? Select all that apply.
- [ ] A. The set is a basis for \(\mathbb{R}^3\).
- [ ] B. The set is linearly independent.
- [ ] C. The set spans \(\mathbb{R}^3\).
- [ ] D. None of the above
---
To solve the question, analyze if the given vectors are linearly independent and if they span the vector space \(\mathbb{R}^3\). A set of three vectors is a basis for \(\mathbb{R}^3\) if it is linearly independent and spans \(\mathbb{R}^3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff5f1b79-f8dc-48a5-a6af-e3b161b5a7d5%2F0114d10f-2631-4c4e-982b-a817513dbd22%2Fhoq2l4_processed.png&w=3840&q=75)
Transcribed Image Text:### Determine Basis and Linear Independence
Determine if the set of vectors shown to the right is a basis for \(\mathbb{R}^3\). If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans \(\mathbb{R}^3\).
\[
\left\{
\begin{bmatrix}
3 \\
-1 \\
1
\end{bmatrix},
\begin{bmatrix}
2 \\
-4 \\
2
\end{bmatrix},
\begin{bmatrix}
-9 \\
6 \\
3
\end{bmatrix}
\right\}
\]
---
### Multiple Choice Question
Which of the following describe the set? Select all that apply.
- [ ] A. The set is a basis for \(\mathbb{R}^3\).
- [ ] B. The set is linearly independent.
- [ ] C. The set spans \(\mathbb{R}^3\).
- [ ] D. None of the above
---
To solve the question, analyze if the given vectors are linearly independent and if they span the vector space \(\mathbb{R}^3\). A set of three vectors is a basis for \(\mathbb{R}^3\) if it is linearly independent and spans \(\mathbb{R}^3\).
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