I assume that f^2 means f(f(x)). So find the matrix that represents f, multiply it by it self and then solve the equation A^2=0, where A is the matrix representing f.
I'm given this linear transformation and I'm asked to do the typical calculations (kernel, image, dimensions, etc.) but there's one thing I'm not sure I understand, here's the exercise:
a) Is f invertible?
b)Find a basis of Ker(f) and a basis of Im(f)
c)Find eigenvalues, eigenvectors. is f diagonalizable?
d) Solve the system f^2(x)=0
Can anybody point me in the right direction on how to solve d) ?
Thanks a lot