Homework SourseLet u 1 0 7 2 v 0 1 0 2 and let W the subspace of R4 spann
Let u = [1 0 7 2], v = [0 1 0 -2], and let W the subspace of R^4 spanned by {u, v}. Find a basis for W ![Let u = [1 0 7 2], v = [0 1 0 -2], and let W the subspace of R^4 spanned by {u, v}. Find a basis for W SolutionLet p= (x,y,z,w)T be an arbitrary element of W.](/WebImages/46/let-u-1-0-7-2-v-0-1-0-2-and-let-w-the-subspace-of-r4-spann-1143867-1761614200-0.webp "Let u = [1 0 7 2], v = [0 1 0 -2], and let W the subspace of R^4 spanned by {u, v}. Find a basis for W SolutionLet p= (x,y,z,w)T be an arbitrary element of W.")
Solution
Let p= (x,y,z,w)T be an arbitrary element of W. Then p.u = 0 or, (x,y,z,w)T.(1,0,7,2)T = 0 or, x +7z +2w = 0.
Also p.v = 0 or, (x,y,z,w)T.(0,1,0,-2)T = 0 or, y-2w = 0. Let z = r and w = t. Then p = (x,y,z,w)T = (-7r-2t, 2t, r,t)T = r (-7,0,1,0)T+t (-2, 2,0,1)T. Hence a basis for W is { (-7,0,1,0)T, (-2, 2,0,1)T}.
