031 Review Part 3, Problem 4

Let  $W={\text{Span }}{\Bigg \{}{\begin{bmatrix}2\\0\\-1\\0\end{bmatrix}},{\begin{bmatrix}-3\\1\\0\\0\end{bmatrix}}{\Bigg \}}.$  Is  ${\begin{bmatrix}2\\6\\4\\0\end{bmatrix}}$  in  $W^{\perp }?$  Explain.

Foundations:
Recall that if  $W$  is a subspace of  $\mathbb {R} ^{n},$  then
$W^{\perp }=\{{\vec {v}}\in \mathbb {R} ^{n}~:~{\vec {v}}\cdot {\vec {w}}=0{\text{ for all }}w\in W\}.$

Solution:

Step 1:

Step 2:

Final Answer:

Return to Sample Exam