et aj = (1,3, –2), a2 = (5,1, 4), and b = (6, –9,3). a) Project b onto the line through aj. b) Project b onto span{aj, a2}, i.e., the subspace spanned by aj and az.

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

4. Let aj — (1, 3, —2), аз — (5, 1,4), and b — (6, —9, 3). %3D (a) Project b onto the line through a1. (b) Project b onto span{a1, a2}, i.e., the subspace spanned by aj and a2.

Find a basis for the two-dimensional subspace of R^4 defined by