True/False: W is a subspace? x2 = 3.x1 12 W

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Concept refers to vector spaces and Linear Algebra and Differential equations 

**True/False: W is a subspace?**

\[ W = \left\{ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \middle| \, x_2 = 3x_1 \right\} \]

Explanation: 

This notation defines a set \(W\) consisting of all 2-dimensional vectors \(\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\) where the second component \(x_2\) is equal to three times the first component \(x_1\). The question posed is whether this set \(W\) forms a subspace.
Transcribed Image Text:**True/False: W is a subspace?** \[ W = \left\{ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \middle| \, x_2 = 3x_1 \right\} \] Explanation: This notation defines a set \(W\) consisting of all 2-dimensional vectors \(\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\) where the second component \(x_2\) is equal to three times the first component \(x_1\). The question posed is whether this set \(W\) forms a subspace.
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