Results 1 to 2 of 2

Math Help - polinomial squared problem

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    polinomial squared problem

    4)A)
    there is A=\left(\begin{array}{ccc}i & 0 & 1\\0 & 3 & 0\\0 & 0 & i\end{array}\right) find polinomial 0\neq Q(t)=at^{2}+bt+c\in C_{3}[t]
    so [Q(A)]^{2}=0
    B)there is A\in M_{nxn}^{F} matrices which is not diagonisable.
    prove that if F=C (the field is C) then there is a polinomial 0\neq Q(t)\in C_{n}[t] so [Q(A)]^{2}=0
    c)
    does the previos part id true if F=R
    ?
    dont knot from where to start,any starting guidence?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: polinomial squared problem

    i solved part A by taking the caracteristic polinomial of A  p(t)=(t-i)^{2}(t-3)
    then we take d(t)=(t-i)(t-3)

    d^{2}(t)=(t-i)^{2}(t-3)^{2}=(t-i)^{2}(t-3)(t-3)

    by cayly hemilton

    p(A)=(A-iI)^{2}(A-3I)=0

    so

    d^{2}(A)=(A-iI)^{2}(A-3I)^{2}=(A-iI)^{2}(A-3I)(A-3I)=0(A-3I)=0

    what is the difference between part A and part B

    why cant i solve it the same way?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. lagrange polinomial methos
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2011, 06:11 AM
  2. chi squared/pearson squared problem 2
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 12th 2010, 05:16 PM
  3. chi squared/pearson squared problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 12th 2010, 05:09 PM
  4. polinomial solution question..
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 3rd 2009, 10:25 AM
  5. Minimal Polinomial
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 3rd 2007, 02:57 PM

Search Tags


/mathhelpforum @mathhelpforum