<s>[INST] Find the rank of the following matrix. $A= \left[ \begin{array}{ccc}
3 & -1 & 2 \\
-6 & 2 & 4 \\
-3 & 1 & 2 \end{array} \right]$
Applying, $R_{3}-\frac{1}{2}R_{2}$
~ $A= \left[ \begin{array}{ccc}
3 & -1 & 2 \\
-6 & 2 & 4 \\
0 & 0 & 0 \end{array} \right]$
Applying, $R_{2}+2R_{1}$
~ $A= \left[ \begin{array}{ccc}
3 & -1 & 2 \\
0 & 0 & 8 \\
0 & 0 & 0 \end{array} \right]$
 [/INST] Row reduce the matrix and count the nonzero rows that remain.
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