corvetx13

The following problem is puzzling me so any help would be appreciated! Consider the linear transformation L: M_22 -> R^4 defined by L of (a b c d) = (-10a - c + 2d, 5a + b - d, 2c + d, 9a + 17b + 2d) Compute ker(L). Okay, so far I've put the matrix: 10 0 -1 2 5 1 0 -1 0 0 2 1 9 17 0 2 into row reduced echelon form to get 1 0 0 -1/4 0 1 0 1/4 0 0 1 1/2 0 0 0 0 And from this, I've gotten that a = 1/4 d b = -1/4 d c = -1/2 d and d is arbitrary But how do I notate ker(L)?