Let T(x) = Ax be a linear transformation where
| 1 -2 3 -1 |
| 3 2 1 1 |
A= | 4 0 4 0 |
|-2 -4 2 -2 |

a) Find the basis for ker(T)
b) Find the basis for range(T)
c) Find a basis for row space of A
d) State the rank of A
e) State the nullity (A)
f) State whether A is invertible

You can use technology to put the matrix A in echelon form, but be sure to give the echelon form because your answer will be graded based on this form.