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Math Help - Linear transformation exercise

  1. #1
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    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
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  2. #2
    Member ModusPonens's Avatar
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    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.
    Thanks from HallsofIvy
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  3. #3
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    Re: Linear transformation exercise

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