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.

Answered: Image /qna-images/answer/0efea727-a881-480c-a006-b775db796275.jpg

Answered: 6. Let T: R³ R³ be the orthogonal…

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. 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.