Hello, this is my matlab hw from linear algebra course. plase provide me with the matlab codes! thank you very much :)

ALSO, a question part marked with a star(*) indicates the answer should be typed into your output as a comment the question isnt asking for MATLAB output.

For this problem, please do e,f,g ONLY. I'll post the rest in a separate question since it is too much.

4. Let W be the subspace of R6 given by 33 25 221 3 01 24 W = Span 1-1 25 19 2 0 0 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. (Hint: Treat W as Col A) (c) Enter your basis for W as the columns of a matrix B. Compute the factorization B = QR with a single command. Give an orthonormal basis for W (d) Let E QQT. As a linear transformation on R6, E is the orthogonal projection onto the subspace w. Use E to compute the orthogonal projection of the vector v (1, 1, 1, 1, 1,1)" 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(BT), so it suffices to find a basis for Nul(B7) (f) As you did for W, find an orthonormal basis for W . (g) Compute the matrix F for the orthogonal projection onto W1. What is the sum E F? 4. Let W be the subspace of R6 given by 33 25 221 3 01 24 W = Span 1-1 25 19 2 0 0 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. (Hint: Treat W as Col A) (c) Enter your basis for W as the columns of a matrix B. Compute the factorization B = QR with a single command. Give an orthonormal basis for W (d) Let E QQT. As a linear transformation on R6, E is the orthogonal projection onto the subspace w. Use E to compute the orthogonal projection of the vector v (1, 1, 1, 1, 1,1)" 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(BT), so it suffices to find a basis for Nul(B7) (f) As you did for W, find an orthonormal basis for W . (g) Compute the matrix F for the orthogonal projection onto W1. What is the sum E F