A set S of vectors in R4 is given. Find a subset of S that forms a basis for the subspace of Rª spanned by S. V₁ = 1 3 - 1 3 V₂ = 2 26 - 22 26 V3 = 5 35 -25 35
A set S of vectors in R4 is given. Find a subset of S that forms a basis for the subspace of Rª spanned by S. V₁ = 1 3 - 1 3 V₂ = 2 26 - 22 26 V3 = 5 35 -25 35
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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![A set \( S \) of vectors in \( \mathbb{R}^4 \) is given. Find a subset of \( S \) that forms a basis for the subspace of \( \mathbb{R}^4 \) spanned by \( S \).
\[
\mathbf{v}_1 = \begin{bmatrix}
1 \\
3 \\
-1 \\
3 \\
\end{bmatrix}, \quad
\mathbf{v}_2 = \begin{bmatrix}
2 \\
26 \\
-22 \\
26 \\
\end{bmatrix}, \quad
\mathbf{v}_3 = \begin{bmatrix}
5 \\
35 \\
-25 \\
35 \\
\end{bmatrix}
\]
A basis for the subspace is given by [ ].
(Use a comma to separate vectors as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a1a8c69-ac20-486b-9f67-8f66504c5494%2F54fa7d2e-8b91-4ebd-906e-68baf0c8df1d%2F6pr7bpd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A set \( S \) of vectors in \( \mathbb{R}^4 \) is given. Find a subset of \( S \) that forms a basis for the subspace of \( \mathbb{R}^4 \) spanned by \( S \).
\[
\mathbf{v}_1 = \begin{bmatrix}
1 \\
3 \\
-1 \\
3 \\
\end{bmatrix}, \quad
\mathbf{v}_2 = \begin{bmatrix}
2 \\
26 \\
-22 \\
26 \\
\end{bmatrix}, \quad
\mathbf{v}_3 = \begin{bmatrix}
5 \\
35 \\
-25 \\
35 \\
\end{bmatrix}
\]
A basis for the subspace is given by [ ].
(Use a comma to separate vectors as needed.)
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