Row space of matrix 
Hello! I am working on some differential equations homework and it is saying that my answer for this question is wrong, and i am not sure as to why. First I reduced the matrix A and then I read the first row of the reduced matrix into the given u=[], and the second row into v=[]. When that answer wasn't correct, I used my calculator to reduce A and got the same answer as when I did it by hand. Maybe I am not approaching this question correct, but if someone can help me solve it i would greatly appreciate it! 

$\begin{equation} \begin{aligned} \pmatrix{ 3 & 3 & 5 & -3 & -2 \\ 2 & 1 & -3 & -1 & 5 \\ 4 & 5 & 13 & -5 & -9} = & \pmatrix{ 3 & 3 & 5 & -3 & -2 \\ 2 & 1 & -3 & -1 & 5 \\ 0 & 3 & 19 & -3 & -19} \\ = & \pmatrix{ 3 & 3 & 5 & -3 & -2 \\ 0 & -1 & -\frac{19}{3} & 1 & \frac{19}{3} \\ 0 & 3 & 19 & -3 & -19} \\ = & \pmatrix{ 3 & 3 & 5 & -3 & -2 \\ 0 & -1 & -\frac{19}{3} & 1 & \frac{19}{3} \\ 0 & 0 & 0 & 0 & 0} \\ = & \pmatrix{ 3 & 0 & -14 & 0 & 17 \\ 0 & -1 & -\frac{19}{3} & 1 & \frac{19}{3} \\ 0 & 0 & 0 & 0 & 0} \\ = & \pmatrix{ 1 & 0 & -\frac{14}{3} & 0 & \frac{17}{3} \\ 0 & 1 & \frac{19}{3} & -1 & -\frac{19}{3} \\ 0 & 0 & 0 & 0 & 0} \end{aligned} \end{equation}$
Is this what you got when you row reduced? I feel like your work is correct.
