6. Let T: R³ R³ be the orthogonal projection onto the line spanned by ( 1 15 Find a basis for which this projection matrix is diagonal, that is, the only nonzero entries occur in the (1,1), (2,2), and (3,3) entries.
6. Let T: R³ R³ be the orthogonal projection onto the line spanned by ( 1 15 Find a basis for which this projection matrix is diagonal, that is, the only nonzero entries occur in the (1,1), (2,2), and (3,3) entries.
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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![6. \( \frac{1}{15} \) Let \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) be the orthogonal projection onto the line spanned by
\[
\begin{pmatrix}
1 \\
1 \\
1
\end{pmatrix}
\].
Find a basis for which this projection matrix is diagonal, that is, the only nonzero entries occur in the (1,1), (2,2), and (3,3) entries.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F474a784e-9f95-4813-81d7-a60d3fc34f86%2F0efea727-a881-480c-a006-b775db796275%2Flgyb6e_processed.png&w=3840&q=75)
Transcribed Image Text:6. \( \frac{1}{15} \) Let \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) be the orthogonal projection onto the line spanned by
\[
\begin{pmatrix}
1 \\
1 \\
1
\end{pmatrix}
\].
Find a basis for which this projection matrix is diagonal, that is, the only nonzero entries occur in the (1,1), (2,2), and (3,3) entries.
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