Solution Found!
Answer: In Exercises 7–10, let W be the subspace spanned
Chapter 6, Problem 9E(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 .
\(\mathbf{y}=\left[\begin{array}{r}4 \\ 3 \\ 3 \\ -1\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{l}1 \\ 1 \\ 0 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}-1 \\ 3 \\ 1 \\ -2\end{array}\right], \mathbf{u}_{3}=\left[\begin{array}{r}-1 \\ 0 \\ 1 \\ 1\end{array}\right]\)
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 .
\(\mathbf{y}=\left[\begin{array}{r}4 \\ 3 \\ 3 \\ -1\end{array}\right], \mathbf{u}_{1}=\left[\begin{array}{l}1 \\ 1 \\ 0 \\ 1\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{r}-1 \\ 3 \\ 1 \\ -2\end{array}\right], \mathbf{u}_{3}=\left[\begin{array}{r}-1 \\ 0 \\ 1 \\ 1\end{array}\right]\)
ANSWER:Solution 9EStep 1 of 3Write the vectors and First verify that is an orthogonal set.The set of vectors is orthogonal if Compute the dot products of the pairs of vectors. Similarly Thus, is an orthogonal set.