6. Let B:{1+2x+3x2,m+x2,1+2as+4332}. 3 is a basis of P2 (the vector space of polynomials of degree at most 2). 2 (a) If [VLB = 3 ,nd v. 51 (b) If w = 2 + 332, nd [w]3. 7. Let B be the basis of P2 given in problem 6, and let S be the standard basis of P2. (a) Find the change of basis matrix P's-+3. (b) Find the change of basis matrix P595. 8. Let A be the matrix 1 2 0 0 4 1 2 1 0 10 A 2 4 1 1 9 5 10 1 1 21 (a) Find a basis for the nullspace of A. What is the dimension of this space? (b) Find a basis for the column space of A. What is the dimension of this space? 9. Let B be the matrix 10113 0 31538 0 3:5174141 6186171 (a) Find a basis for the nullspace of B. What is the dimension of this space? (b) Find a basis for the column space of B. What is the dimension of this space