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The orthogonal projection of the vector u = 2 on the subspace V 1 is ... [7/3 5/3 8/3 = span (0-4)

The orthogonal projection of the vector u = 2 on the subspace V 1 is ... [7/3 5/3 8/3 = span (0-4)

Advanced Engineering Mathematics
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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The problem given is: "The orthogonal projection of the vector \(\mathbf{u} = \begin{bmatrix} 4 \\ 2 \\ 1 \end{bmatrix}\) on the subspace \(V = \text{span}\left(\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}\right)\) is..." There are four multiple-choice answers provided: 1. \(\begin{bmatrix} 7/3 \\ 5/3 \\ 8/3 \end{bmatrix}\) 2. \(\begin{bmatrix} 13/6 \\ 7/6 \\ 11/6 \end{bmatrix}\) 3. \(\begin{bmatrix} 23/6 \\ 14/6 \\ 5/6 \end{bmatrix}\) 4. \(\begin{bmatrix} 4 \\ 2 \\ 3 \end{bmatrix}\) This is a linear algebra problem that involves computing the orthogonal projection of a vector onto a subspace defined by the span of other vectors.
Transcribed Image Text:The problem given is: "The orthogonal projection of the vector \(\mathbf{u} = \begin{bmatrix} 4 \\ 2 \\ 1 \end{bmatrix}\) on the subspace \(V = \text{span}\left(\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}\right)\) is..." There are four multiple-choice answers provided: 1. \(\begin{bmatrix} 7/3 \\ 5/3 \\ 8/3 \end{bmatrix}\) 2. \(\begin{bmatrix} 13/6 \\ 7/6 \\ 11/6 \end{bmatrix}\) 3. \(\begin{bmatrix} 23/6 \\ 14/6 \\ 5/6 \end{bmatrix}\) 4. \(\begin{bmatrix} 4 \\ 2 \\ 3 \end{bmatrix}\) This is a linear algebra problem that involves computing the orthogonal projection of a vector onto a subspace defined by the span of other vectors.
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