Find a basis B for the span of the given vectors. 3 0 HG 0 1
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
![Find a basis **B** for the span of the given vectors.
\[
\begin{bmatrix}
3 \\
-1 \\
0
\end{bmatrix}, \quad
\begin{bmatrix}
-3 \\
0 \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
0 \\
1 \\
-1
\end{bmatrix}
\]
**B** = \{
\[
\begin{bmatrix}
\phantom{3} \\
\phantom{-1} \\
\phantom{0}
\end{bmatrix}
\],
\[
\begin{bmatrix}
\phantom{-3} \\
\phantom{0} \\
\phantom{1}
\end{bmatrix}
\]
\}
### Explanation:
The image asks to find a basis **B** for the span of the given vectors. It provides three column vectors and an empty structure to fill in with the appropriate basis vectors. The basis vectors are found by evaluating the linear independence of the original vectors and selecting a set that spans the same space without redundancy.
The diagram below the vectors represents placeholders for the basis vectors, indicating that two or more vectors may form the basis, depending on their linear relationship. The symbols such as arrows suggest action steps or rearrangement to identify the correct basis from the vectors provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6948d5d-782c-4f32-af22-abf47b4c3397%2Fe98298ea-50d8-429f-bb05-c8c04f8b09d8%2Fz50dloe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find a basis **B** for the span of the given vectors.
\[
\begin{bmatrix}
3 \\
-1 \\
0
\end{bmatrix}, \quad
\begin{bmatrix}
-3 \\
0 \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
0 \\
1 \\
-1
\end{bmatrix}
\]
**B** = \{
\[
\begin{bmatrix}
\phantom{3} \\
\phantom{-1} \\
\phantom{0}
\end{bmatrix}
\],
\[
\begin{bmatrix}
\phantom{-3} \\
\phantom{0} \\
\phantom{1}
\end{bmatrix}
\]
\}
### Explanation:
The image asks to find a basis **B** for the span of the given vectors. It provides three column vectors and an empty structure to fill in with the appropriate basis vectors. The basis vectors are found by evaluating the linear independence of the original vectors and selecting a set that spans the same space without redundancy.
The diagram below the vectors represents placeholders for the basis vectors, indicating that two or more vectors may form the basis, depending on their linear relationship. The symbols such as arrows suggest action steps or rearrangement to identify the correct basis from the vectors provided.
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