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Solved: In Exercises 7–10, let W be the subspace spanned
Chapter 6, Problem 8E(choose chapter or problem)
In Exercises 7–10, let W be the subspace spanned by the u’s, and write y as the sum of a vector in W and a vector orthogonal to W .
\(\mathbf{y}=\left[\begin{array}{r}-1 \\ 4 \\ 3\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}-1 \\ 3 \\ -2\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 7–10, let W be the subspace spanned by the u’s, and write y as the sum of a vector in W and a vector orthogonal to W .
\(\mathbf{y}=\left[\begin{array}{r}-1 \\ 4 \\ 3\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}-1 \\ 3 \\ -2\end{array}\right]\)
ANSWER:Solution 8EStep 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.