(6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the distance from y to span{u1, u2}?
(6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the distance from y to span{u1, u2}?
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
\[
\mathbf{y} = \begin{pmatrix} -1 \\ 2 \\ 6 \end{pmatrix}
\]
and
\[
\mathbf{u_1} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}, \quad \mathbf{u_2} = \begin{pmatrix} 1 \\ -1 \\ -2 \end{pmatrix}.
\]
Find the closest point to \(\mathbf{y}\) in \(\text{span}\{\mathbf{u_1}, \mathbf{u_2}\}\). What is the distance from \(\mathbf{y}\) to \(\text{span}\{\mathbf{u_1}, \mathbf{u_2}\}\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bd9bd0-40fd-4172-a50a-abb52eb6a8c1%2F077c8381-8b06-46a5-b62b-38f3145a11ce%2Fnm847bk_processed.png&w=3840&q=75)
Transcribed Image Text:Let
\[
\mathbf{y} = \begin{pmatrix} -1 \\ 2 \\ 6 \end{pmatrix}
\]
and
\[
\mathbf{u_1} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}, \quad \mathbf{u_2} = \begin{pmatrix} 1 \\ -1 \\ -2 \end{pmatrix}.
\]
Find the closest point to \(\mathbf{y}\) in \(\text{span}\{\mathbf{u_1}, \mathbf{u_2}\}\). What is the distance from \(\mathbf{y}\) to \(\text{span}\{\mathbf{u_1}, \mathbf{u_2}\}\)?
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