Find a basis for each of the subspaces.

1. The subspace R^5 given by the solution space of the homogeneous system system

2x_1+2x_2-x_3+x_5=0

-x_1-x_2+2x_3-3x_4+x_5=0

x_1+x_2-2x_3-x_5=0

x_3+x_4+x_5=0.

2. The subspace of R^6 given by

W={(u,v,w,x,y,z) in R^6: u+w=v-x, v=y+z}