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Homework Help: Anyone can prove this ?

  1. Jan 24, 2010 #1
    1. show that if a square matrix A satisfies A^3+4A^2 -2A+7i=0 then so does A^T

    i is the identity matrix






    3. The attempt at a solution

    I tried to multiply the equation by A^T but all in vain
     
  2. jcsd
  3. Jan 24, 2010 #2
    Use:
    [tex](A+B)^T = A^T + B^T \qquad (AB)^T = A^TB^T \qquad (cA)^T = cA^T[/tex]
    to compute the transpose by using:
    [tex]0 = 0^T = (A^3 + 4A^2 - 2A + 7I)^T[/tex]
     
  4. Jan 24, 2010 #3
    thanks
    this is useful

    problem solved:biggrin:
     
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