Recent content by universedrill

  1. U

    How can we prove that a nxn real matrix A is a root of a given polynomial?

    Thanks, but I don't understand clearly what you mean. And, is there any solution where theorem 1 isn't used for problem 2?
  2. U

    How can we prove that a nxn real matrix A is a root of a given polynomial?

    Homework Statement 1) Prove that: nxn real matrix A is a root of f(X)= a[n].X^n+...+a[0].I, where a[n],...,a[0] are coefficients of the polynomial P(t)= det [A-t.I] 2) Let 5x5 real matrix A be satisfied: A^2008 = 0. Prove that: A^5=0. 2. The attempt at a solution I tried to solve problem...
  3. U

    Linear Algebra - Determinant Properties

    Please help me with these: 1) Prove that: nxn real matrix A is a root of f(X)= a[n].X^n+...+a[0].I, where a[n],...,a[0] are coefficients of the polynomial P(t)= det [A-t.I] 2) Let 5x5 real matrix A be satisfied: A^2008 = 0. Prove that: A^5=0. Thanks.