Let vector u 0 1 4 0 vector v 0 0 0 1 and let W the subspa

Let vector u = [0 1 4 0], vector v = [0 0 0 1], and let W the subspace of R^4 spanned by{vector u, vector v}. Find a basis for W^

Solution

Let, x=[r s t u] be in W\'

SO, x.u=0

s+4t=0

s=-4t

x.v=0 which gives:u=0

x=[r -4t t 0]=r[ 1 0 0 0]+t[0 4 1 0]

Basis =

{(1,0,0,0),(0,4,1,0)}