Assignment: determining sets are bases of $\mathbb{R}^3$ This is question from an assignment I'm working on:

Which two of the following three sets in $\mathbb{R}^3$ is a basis of $\mathbb{R}^3$?
\begin{align*}
B_1&=\{(1,0,1),(6,4,5),(-4,-4,7)\}\\
B_2&=\{(2,1,3),(3,1,-3),(1,1,9)\}\\
B_3&=\{(3,-1,2),(5,1,1),(1,1,1)\}
\end{align*}

Thanks to software, I know that the answer is $B_1$ and $B_3$, as $B_2$ the only linearly dependent set of the three - and in this case, an LD set can't be a basis for $\mathbb{R}^3$.
Manually, I've put all three sets in RREF, and all three can be reduced to
$$
\left[\begin{array}{ccc|c}
{1}&{0}&{0}&{0}\\
{0}&{1}&{0}&{0}\\
{0}&{0}&{1}&{0}
\end{array}\right]
$$
This also checks out when computed by software.
Since all three sets reduce to the same RREF, how can I prove that these sets are linearly (in)dependent?

Let V={$v_1,v_2,...,v_n$} be a set of n vectors in $\mathbb{R}^n$. then V is linearly independent iff the matrix A=($v_1,v_2,...,v_n$) is invertible where v_i is the ith column of A . proving this result is an easy exercise
. 
