(3+5+2+4+4+4 22 points) Let A= [1 1 1] [1 1 1]
[0 1 1]
[0 1 1]

Required:
a. Find a basis for the column space of A. What is the dimension of this basis?
b. Use Gram-Schmidt to find an orthonormal basis for the column space of A: {q1, q2, q3}
c. Find a fourth vector q4 that completes the basis you have found in part (a) to an orthonormal basis of R4. To which of the 4 fundamental spaces related to A does q4 belong to?
d. Find the projection matrix P that maps any vector onto C(A). What is the projection of b= (1, 0, 0,0) onto this space?