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  1. J

    Characteristic and Minimal polynomials of matrices

    Homework Statement Let V=C^4 and consider the linear map V->V given by the matrix: {{12,-6,6,-6},{2,21,21,51},{-3,12,12,30},{1,-9,-9,-21}} (Each {...} denotes a row, tried to use Latex but got extremely confused!) Given that chA(X)=(X-6)^4, calculate: (i) The power such that...
  2. J

    Linear maps: finding matrix

    Homework Statement Let T:R[x]2->R[x]3 be defined by T(P(x))=xP(x). Compute the matrix of T with respect to bases {1,x,x^2} and {1,x,x^2,x^3}. Find the kernel and image of T. The Attempt at a Solution I genuinely have no idea where to start on this, any pointers you can give me would be...