Quick question on trying to write the following matrix in parametric vector form:

A = [[1, -3, 0, -2, 4], [0, 0, 1, 5, -2], [0, 0, 0, 0, 0]]

(So it's a 3x5 matrix)...

So I started out by saying:

x_1 = 3x_2 + 2x_4 + 4

x_3 = -5x_4 -2

Then:

x_2*[0, 3, 0, 0] + x_4 [0, 0, 0, 2] <-- but the problem is I have an x_4 in the other equation too. Should I maybe solve up above for the free variables, instead of x_1, x_3?