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Homework Help: Kernel of linear transformation

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    I am having lots of trouble understanding how to get the kernel of linear transformations. I get that you basically set it equal to zero and solve.

    T: P3 → P2 given by T(p(x)) = p΄΄(x) + p΄(x) + p(0)

    Find ker(T)

    3. The attempt at a solution

    So P3 = ax^3 + bx^2 + cx +d
    then the linear transformation should be

    6ax + 2b + 3ax2 + 2bx + c + d

    but how do i find ker T?
  2. jcsd
  3. Oct 27, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    You've got the transformation right. You want the result to be a zero polynomial. A polynomial is only zero if the coefficient of each power of x is zero.
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