9000019904

The coefficient matrix of a $3\times 3$ linear system is $A$ and the augmented matrix $A^{\prime }$. Find $\mathrm{rank}(A)$ and $\mathrm{rank}(A^{\prime })$. $$A=\left(\begin{array}{ccc}-1& 3& 2\\ 0& 4& -5\\ 0& 0& 2\end{array}\right)A^{\prime }=\left(\begin{array}{cccc}-1& 3& 2& 5\\ 0& 4& -5& 10\\ 0& 0& 2& 0\end{array}\right)$$