Question

Given vectors v1=[3 2 1 ]T and v2=[-6 3 0] , describe the sub space W subset of V that has v1 and v2 as its basis vectors

Answer 1

\[\left| \left(\begin{matrix}3 \\ 2 \\ 1\end{matrix}\right)\times \left(\begin{matrix}-6 \\ 3 \\ 0\end{matrix}\right) \right|=\left| \left(\begin{matrix}-3 \\ -6 \\9+12\end{matrix}\right) \right|=\left| \left(\begin{matrix}-3 \\ -6 \\ 21\end{matrix}\right) \right|=\sqrt{3^{2}+6^{2}+21^{2}}\]
\[=\sqrt{9+36+441}=\sqrt{486}=3 \times \sqrt{54}=9 \times \sqrt{6}\]

Answer 2

I did not understand , i want to show how W is sub set of V geometrically