Results 1 to 2 of 2

Math Help - Determinant

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    7

    Determinant

    Assuming Det(AB) = Det(A) x Det(B) for 3x3 matrices prove that the determinant of

    3 , a+b+c , a^3+b^3+c^3
    a+b+c , a^2+b^2+c^2 , a^4+b^4+c^4
    a^2+b^2+c^2 , a^3+b^3+c^3 , a^5+b^5+c^5

    = (a+b+c)(b-a)^2(c-a)^2(a-b)^2

    i was just going to work through the math but i dont really understand how the result given at the top will help me when working out the determinant as its is the cofactor times the 2x2 you get - the next cofactor times the 2x2 and so on.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hi,
    Quote Originally Posted by rebirthflame View Post
    Assuming Det(AB) = Det(A) x Det(B) for 3x3 matrices prove that [...]

    \begin{vmatrix}<br />
3                   & a+b+c           & a^3+b^3+c^3\\<br />
a+b+c            & a^2+b^2+c^2 & a^4+b^4+c^4\\ <br />
a^2+b^2+c^2 & a^3+b^3+c^3 & a^5+b^5+c^5\\<br />
\end{vmatrix}<br />
= (a+b+c)(b-a)^2(c-a)^2(a-b)^2
    I suggest you try to find two matrices A and B such that
    AB=\begin{pmatrix}<br />
3                   & a+b+c           & a^3+b^3+c^3\\<br />
a+b+c            & a^2+b^2+c^2 & a^4+b^4+c^4\\ <br />
a^2+b^2+c^2 & a^3+b^3+c^3 & a^5+b^5+c^5\\<br />
\end{pmatrix}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Determinant
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 14th 2010, 11:26 AM
  2. Determinant help
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 16th 2010, 12:55 AM
  3. Determinant
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 10th 2009, 06:24 PM
  4. Determinant 3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 28th 2009, 11:53 AM
  5. Determinant 2
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 28th 2009, 01:34 AM

Search Tags


/mathhelpforum @mathhelpforum