Linear transformation exercise

Hello,

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:

f(1,0,0)=(-1,-2,-3)

f(0,1,0)=(2,2,2)

f(0,0,1)=(0,1,2)

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

Re: Linear transformation exercise

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.

Re: Linear transformation exercise

Hello, ModusPonens, thank you for your answer, I get it :)