Results 1 to 4 of 4

Math Help - Polynomial

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    195
    Thanks
    1

    Polynomial

    |-1 0 0 0|
    |0 -1 3 0|
    |0 0 2 0|
    |-3 3 -3 2|

    Given this matrix A, and the polynom f(x) = x^2 + x + 2, what is the matrix M = f(A) ? Thanks alot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by gralla55 View Post
    |-1 0 0 0|
    |0 -1 3 0|
    |0 0 2 0|
    |-3 3 -3 2|

    Given this matrix A, and the polynom f(x) = x^2 + x + 2, what is the matrix M = f(A) ? Thanks alot!

     \left[\begin{array}{cccc}-1&0&0&0\\0&-1&3&0\\0&0&2&0\\-3&3&-3&2\end{array}\right]

    f(x)= x^2 + x +2

    f(A) = A^2 + A + 2I I is the identity

    f(A) =\left[\begin{array}{cccc}-1&0&0&0\\0&-1&3&0\\0&0&2&0\\-3&3&-3&2\end{array}\right]\times \left[\begin{array}{cccc}-1&0&0&0\\0&-1&3&0\\0&0&2&0\\-3&3&-3&2\end{array}\right] + \left[\begin{array}{cccc}-1&0&0&0\\0&-1&3&0\\0&0&2&0\\-3&3&-3&2\end{array}\right] + 2 \left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&  0&1\end{array}\right]<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    195
    Thanks
    1
    Thanks alot! If I did it right, the squared matrix should be:

    1 0 0 0
    0 1 3 0
    0 0 4 0
    -3 3 -3 4

    which makes the final matrix:

    2 0 0 0
    0 2 6 0
    0 0 8 0
    -6 6 -6 8

    Does this look correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    it is correct
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 23rd 2011, 06:36 AM
  2. Replies: 1
    Last Post: February 24th 2011, 06:46 PM
  3. Replies: 1
    Last Post: December 15th 2009, 07:26 AM
  4. [SOLVED] dividing polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 3rd 2008, 02:00 PM
  5. dividing a polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 2nd 2005, 12:26 AM

Search Tags


/mathhelpforum @mathhelpforum