A = 0 -2 0 0 1 (e) Is v = 0 0 0 -1 0 0 0 -3 0 0 -9 1 0 0 0 0 0 0 0 6 (a) Using any method, calculate the determinant of A, det(A). (b) Why is the matrix invertible? (c) If B, C are both 5 × 27 matrices such that AB = C explain why B and C are row equivalent. (d) How many solutions does Ax = 0 have? Why? 2 3 in the column space of A? If so, how many ways are there to write v 4 5 as a linear combination of A's column vectors? (f) Extra Credit: Calculate the adjoint and the inverse of A.