Let {a, b, c} be a set of vectors in R5 defined by 1 -1 1 ; b= -1 a = С — 1 1 and define W by W = {x € IR° : x.a = 0, x b = 0 and x c = 0}- Compute dim(W).
Let {a, b, c} be a set of vectors in R5 defined by 1 -1 1 ; b= -1 a = С — 1 1 and define W by W = {x € IR° : x.a = 0, x b = 0 and x c = 0}- Compute dim(W).
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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![Let \(\{ \mathbf{a}, \mathbf{b}, \mathbf{c} \}\) be a set of vectors in \(\mathbb{R}^5\) defined by
\[
\mathbf{a} = \begin{bmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 1 \end{bmatrix}; \quad \mathbf{b} = \begin{bmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 1 \end{bmatrix}; \quad \mathbf{c} = \begin{bmatrix} 1 \\ 0 \\ -1 \\ -1 \\ 0 \end{bmatrix}.
\]
and define \(W\) by
\[
W = \{ \mathbf{x} \in \mathbb{R}^5 : \mathbf{x} \cdot \mathbf{a} = 0, \; \mathbf{x} \cdot \mathbf{b} = 0 \text{ and } \mathbf{x} \cdot \mathbf{c} = 0 \}
\]
Compute \(\dim(W)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb7f1ce8-2552-49b5-ba1d-534a58de11ae%2F3348f4af-2865-4687-9ed5-f06c874eeac9%2F5drvy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \(\{ \mathbf{a}, \mathbf{b}, \mathbf{c} \}\) be a set of vectors in \(\mathbb{R}^5\) defined by
\[
\mathbf{a} = \begin{bmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 1 \end{bmatrix}; \quad \mathbf{b} = \begin{bmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 1 \end{bmatrix}; \quad \mathbf{c} = \begin{bmatrix} 1 \\ 0 \\ -1 \\ -1 \\ 0 \end{bmatrix}.
\]
and define \(W\) by
\[
W = \{ \mathbf{x} \in \mathbb{R}^5 : \mathbf{x} \cdot \mathbf{a} = 0, \; \mathbf{x} \cdot \mathbf{b} = 0 \text{ and } \mathbf{x} \cdot \mathbf{c} = 0 \}
\]
Compute \(\dim(W)\).
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