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Solution: In Exercises 3–6, verify that {u1, u2} is an
Chapter 6, Problem 6E(choose chapter or problem)
In Exercises 3–6, verify that {\(u_1, u_2\)} is an orthogonal set, and then find the orthogonal projection of y onto Span {\(u_1, u_2\)}.
\(\mathbf{y}=\left[\begin{array}{l}6 \\ 4 \\ 1\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}-4 \\ -1 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 3–6, verify that {\(u_1, u_2\)} is an orthogonal set, and then find the orthogonal projection of y onto Span {\(u_1, u_2\)}.
\(\mathbf{y}=\left[\begin{array}{l}6 \\ 4 \\ 1\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}-4 \\ -1 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\)
ANSWER:Solution 6EStep 1 of 3Write the vectors and First verify that is an orthogonal set.Compute the dot products of the vectors. Thus, is an orthogonal set.