Dordt College Dr. Gary De Young's Website
Contents

Probelm set M

  • Define a sequence a_n for positive integers, n by a_1=1, and a_{n+1} = 3a_n +5 for each n\geq 2. Find an explicit formula for a_n in terms of n.

  • Let A and B be different matrices with real coefficients. if A^3=B^3 and A^2B = B^2A can A^2+B^2 be invertable?
  • Let p(x) be a polynomial with real coefficients prove that if
    p(x) - p^\prime(x) - p^{\prime\prime}(x) + p^{\prime\prime\prime}(x) \ge 0
    for all real x then p(x) \ge 0 for all x
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