**Orthogonal Projection of a Vector onto a Subspace****Problem:**Find the orthogonal projection \( \hat{y} \) of the vector \[ \mathbf{y} = \begin{bmatrix} 5 \\ 0 \\ -5 \end{bmatrix} \]onto the subspace \( W \), which is spanned by the vectors \[ \mathbf{u}_1 = \begin{bmatrix} -1 \\ 4 \\ 6 \end{bmatrix}, \quad \mathbf{u}_2 = \begin{bmatrix} 2 \\ -4 \\ 3 \end{bmatrix} \].**Solution:**The orthogonal projection \( \hat{y} \) is calculated by projecting \( \mathbf{y} \) onto the subspace spanned by \( \mathbf{u}_1 \) and \( \mathbf{u}_2 \).**Answer Input Boxes:**This section allows for the input of the calculated orthogonal projection \( \hat{y} \) in vector form, which is not displayed here for user input.Each component of the vector should be entered into its respective box.**Note:**To solve this problem, use the Gram-Schmidt process to orthogonalize the basis vectors, if necessary, and then use the formula for the orthogonal projection of a vector onto a subspace.

Answered: d the orthogonal projection ŷ of y = 5…

d the orthogonal projection ŷ of y = 5 0 -5 = = Span u₁ = {-----})}) 4 , = 2 -4 onto the 3

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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