A question in understanding a mistake

[transgalactic]

http://img88.imageshack.us/my.php?image=img86311lj7.jpg
(traverse is a typing mistake i ment transpose)

i am given an operator with parameters (the original matrix)
and i was told to find
for which values of a b c
we have the maximal dim ker t
and the the maximal dim I am t

the person who solved it ,
in the ker part he makes an equation with 0

and in the I am part he transposes the matrix and looks for what value of the parameters
we have the maximal amount of independent vectors

so why the teacher written a mistake in both parts??

 

[transgalactic]

can you tell me if you agree with me
or you don't understand the question
i'll refrase it
if needed