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Solved: PROBLEM 21E Does {v1, v2, v3} span 4 Why or why
Chapter 1, Problem 21E(choose chapter or problem)
Let \(\mathbf{v}_{1}=\left[\begin{array}{r}1 \\ 0 \\ -1 \\ 0\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}0 \\ -1 \\ 0 \\ 1\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}1 \\ 0 \\ 0 \\ -1\end{array}\right]\).
Does \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}\) span \(\mathbb{R}^{4}\)? Why or why not?
Questions & Answers
QUESTION:
Let \(\mathbf{v}_{1}=\left[\begin{array}{r}1 \\ 0 \\ -1 \\ 0\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}0 \\ -1 \\ 0 \\ 1\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}1 \\ 0 \\ 0 \\ -1\end{array}\right]\).
Does \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}\) span \(\mathbb{R}^{4}\)? Why or why not?
ANSWER:Solution Step 1:Given three vectors = = = We have to find does {v1, v2, v3} span 3