Answer
See answer below
Work Step by Step
We are given:
$v_1=(0,6,3)$
$v_2=(3,0,3)$
$v_3=(6,-3,0)$
We obtain:
$\begin{vmatrix}
0 & 3 & 6\\
6 & 0 & -3\\
3 & 3 & 0
\end{vmatrix}=0-3\begin{vmatrix}
6 & -3 \\
3 & 0
\end{vmatrix}+6\begin{vmatrix}
6 & 0 \\
3 & 3
\end{vmatrix}=-3[0-(-9)]+6(18-0)=81 \ne 0$
We can say the set of vectors $\{v_1,v_2,v_3\}$ is linearly independent in $R^3$
Since $dim R^3=3$, we have the set $\{v_1,v_2,v_3\}$ is a basis for $R^3$
