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Solution: In Exercises 7–10, let W be the subspace spanned
Chapter 6, Problem 10E(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 .
\(\mathbf{y}=\left[\begin{array}{l}3 \\ 4 \\ 5 \\ 6\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}1 \\ 1 \\ 0 \\ -1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{l}1 \\ 0 \\ 1 \\ 1\end{array}\right], \mathbf{u}_{3}=\left[\begin{array}{r}0 \\ -1 \\ 1 \\ -1\end{array}\right]\)
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 .
\(\mathbf{y}=\left[\begin{array}{l}3 \\ 4 \\ 5 \\ 6\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{r}1 \\ 1 \\ 0 \\ -1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{l}1 \\ 0 \\ 1 \\ 1\end{array}\right], \mathbf{u}_{3}=\left[\begin{array}{r}0 \\ -1 \\ 1 \\ -1\end{array}\right]\)
ANSWER:Solutio