If you are only able to answer 1 question, please answer no.8, I think these questions have connections with each other. Also please answer it ASAP, thank you.

Let A = for Questions 6,7,8. OOI'H OI'I'H |||||'I' 6. (a) Find a basis for the column space of A. What is the dimension of the column space? (b) Use Gram-Schmidt to nd an orthonormal basis for the column space of A: {517 (f2) (13}- 7. (a) Find a fourth vector Q7; that completes the basis you have found in Question 6.(a) to an orthonormal basis of R4. (Hint: To Which of the 4 fundamental spaces related to A does (j; belong to?) (b) Find the projection matrix P that maps any vector onto 0 (A) using the or- thonormal basis in Question 6.(b). What is the projection of E = (1, 0,0,0) onto this space? 8. (a) Find the factorization A = QR Where Q has orthonormal columns and R is upper triangular. Check that R is invertible. (b) Find the best least-squares solution to A5 = , using the result of 1 0 0 0 Question 8(a)