# Thread: Basis for a subspace and dimension

1. ## Basis for a subspace and dimension

Find a basis for the subspace W of R^5 given by...

W = {x E R^5 : x . a = x . b = x . c = 0}, where a = (1, 0, 2, -1, -1), b = (2, 1, 1, 1, 0) and c = (4, 3, -1, 5, 2).

Determine the dimension of W. (as usual, "x . a" denotes the dot (inner) product of the vecotrs x and a).