Let WC R4 be a subspace such that W = span(w₁, W2, W3, W4), where 4 1 2 0 W1 = 1 0 1 0 9 W2 = 2 3 1 1 W3 = 0 2 1 1 W4 =
Let WC R4 be a subspace such that W = span(w₁, W2, W3, W4), where 4 1 2 0 W1 = 1 0 1 0 9 W2 = 2 3 1 1 W3 = 0 2 1 1 W4 =
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 the dimension of W, dim(W), and briefly justify your answer.
![Let \( W \subseteq \mathbb{R}^4 \) be a subspace such that \( W = \text{span}(\mathbf{w_1}, \mathbf{w_2}, \mathbf{w_3}, \mathbf{w_4}) \), where:
\[
\mathbf{w_1} = \begin{bmatrix}
1 \\
0 \\
1 \\
0
\end{bmatrix},
\quad
\mathbf{w_2} = \begin{bmatrix}
2 \\
3 \\
1 \\
1
\end{bmatrix},
\quad
\mathbf{w_3} = \begin{bmatrix}
0 \\
2 \\
1 \\
1
\end{bmatrix},
\quad
\mathbf{w_4} = \begin{bmatrix}
4 \\
1 \\
2 \\
0
\end{bmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9612546f-987e-4906-abd4-8f6ba2df88e4%2Fdb81e3f6-5233-4fc5-9480-8742ff0ae009%2Fg7fratn_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( W \subseteq \mathbb{R}^4 \) be a subspace such that \( W = \text{span}(\mathbf{w_1}, \mathbf{w_2}, \mathbf{w_3}, \mathbf{w_4}) \), where:
\[
\mathbf{w_1} = \begin{bmatrix}
1 \\
0 \\
1 \\
0
\end{bmatrix},
\quad
\mathbf{w_2} = \begin{bmatrix}
2 \\
3 \\
1 \\
1
\end{bmatrix},
\quad
\mathbf{w_3} = \begin{bmatrix}
0 \\
2 \\
1 \\
1
\end{bmatrix},
\quad
\mathbf{w_4} = \begin{bmatrix}
4 \\
1 \\
2 \\
0
\end{bmatrix}.
\]
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