use Matlab to solve number 9

Let W be the subspace of R^6 given by W = {[1 0 4 -1 0 2], [3 2 0 5 2 -2], [3 2 1 0 5 0], [5 3 4 -3 9 2]} (a) Enter those five vectors as the columns of a matrix A and compute its rank. (b) The previous computation shows that the five vectors are linearly dependent, hence they do not form a basis for W. Find a basis for W. (c) Enter your basis for W as the columns of a matrix B. Compute the factorized B = QR with a single command. Give an orthonormal basis for W. (d) Let E = QQ^T, As a linear transformation on R^6, E is the orthogonal projection onto the subspace W. Use E to compute the orthogonal projection of the curve v = (1, 1, 1, 1, 1, 1)^t onto W. (e) Find a basis for W as follows. Note that W = Col A = Col B. From a theorem in class, we have W (Col B)^= Nul (B^). so it suffices to find a basis for Nul(B^T). (f) As you did for W, find an orthonormal basis for W (g) Compute the matrix F for the orthogonal projection onto W What is the sum E + F? Consider the inconsistent linear system