Consider the following. W = {(3t, t, -t): t is a real number} (a) Give a geometric description of the subspace W of R³. O a line a ray O a circle a point O a plane (b) Find a basis for the subspace W of R³. - } (c) Determine the dimension of the subspace W of R³.

2

8

The set = 211 {(2a, b, a - b): a, b = R} 0,00) quo & jon ai & Jon ai (o.A) toda wodewoled ol is a subspace of R³. (a) Show that B = {(2, 1, 0), (2, 2, -1)} is a basis for S. (b) Is S a point, a line, a plane or R³ itself? (c) Use Gram-Schmidt orthogonalisation to find an orthogonal basis for S that includes the vector (2, 1,0). ai deda odmun oduo ovidiecq to och