Try constructing a matrix and row-reduce the matrix to find the number of free parameters. Then take that and construct a basis using the free parameters.
Hi,
what is the best way to find the basis of subspace V(x,y,z,w) which is an element of R^4 for 2x-y=z-3w
This is the same as z= 2x- y+ 3w. Such a vector can be written as <x, y, z, w>= <x, y, 2x- y+3w, w>= <x, 0, 2x, 0>+ <0, y, -y, 0>+ <0, 0, 3w, w>= x<1, 0, 2, 0>+ y<0, 1, -1, 0>+ w<0, 0, 3, 1>.
From that it should be obvious what a basis is and what the dimension is.