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Answer: In Exercises 3–6, verify that {u1, u2} is an
Chapter 6, Problem 5E(choose chapter or problem)
In Exercises 3–6, verify that \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}\) is an orthogonal set, and then find the orthogonal projection of y onto Span \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}\).
\(\mathbf{y}=\left[\begin{array}{r}-1 \\ 2 \\ 6\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}3 \\ -1 \\ 2\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}1 \\ -1 \\ -2\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 3–6, verify that \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}\) is an orthogonal set, and then find the orthogonal projection of y onto Span \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}\).
\(\mathbf{y}=\left[\begin{array}{r}-1 \\ 2 \\ 6\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}3 \\ -1 \\ 2\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}1 \\ -1 \\ -2\end{array}\right]\)
ANSWER:Solution 5EStep 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.