9000019905

Let $A$ and $A^{\prime }$ be the coefficient matrix and the augmented matrix of the following linear system, respectively. Find the ranks of these matrices. $$\begin{array}{cl}\phantom{-}3x+5y+\phantom{2}z=\phantom{-}10& \\ -2x-3y+2z=-10& \\ \phantom{-2}x+\phantom{2}y-5z=\phantom{-}10& \end{array}$$