Part I 0. Let a = 2 | and b . The projection of b onto the 2 4 subspace spanned by a is p = The error vector is e = b – p = The dot product of a and e is The matrix that projects vectors onto the subspace spanned by a is P = Part II 1 1 Let A = 2 3 The matrix that projects vectors onto the column 2 2 space of A is P =

Find the dimension of the subspace spanned by the given vectors. - 2 11 8 1 4 - 3 3 - 5 - 29 21

13 Put bases for the subspaces V and W into the columns of matrices V and W. Explain why the test for orthogonal subspaces can be written VTW = zero matrix. This matches vw = 0 for orthogonal vectors.