Let U = span{u₁, U₂}and W = span{w₁, W₂} be subspaces of R³ such that 1 2 0,4₂ = 1 1 3 Fina a vector x E UNW such that x = 0 U₁ = and 2 1 W₁ = 0, W₂ = 1 0 -2
Let U = span{u₁, U₂}and W = span{w₁, W₂} be subspaces of R³ such that 1 2 0,4₂ = 1 1 3 Fina a vector x E UNW such that x = 0 U₁ = and 2 1 W₁ = 0, W₂ = 1 0 -2
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 \( U = \text{span}\{u_1, u_2\} \) and \( W = \text{span}\{w_1, w_2\} \) be subspaces of \( \mathbb{R}^3 \) such that
\[
u_1 = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}, u_2 = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} \quad \text{and} \quad w_1 = \begin{bmatrix} 2 \\ 0 \\ 0 \end{bmatrix}, w_2 = \begin{bmatrix} 1 \\ 1 \\ -2 \end{bmatrix}
\]
Find a vector \( x \in U \cap W \) such that \( x \neq 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98b6e310-08ba-4e1d-a9bc-704b45d2ce6c%2Ff6075f30-6230-4e12-b212-1f4ab2fe7dcc%2F4kz1wvm_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( U = \text{span}\{u_1, u_2\} \) and \( W = \text{span}\{w_1, w_2\} \) be subspaces of \( \mathbb{R}^3 \) such that
\[
u_1 = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}, u_2 = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} \quad \text{and} \quad w_1 = \begin{bmatrix} 2 \\ 0 \\ 0 \end{bmatrix}, w_2 = \begin{bmatrix} 1 \\ 1 \\ -2 \end{bmatrix}
\]
Find a vector \( x \in U \cap W \) such that \( x \neq 0 \).
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