Results 1 to 2 of 2

Math Help - Need help with determinant of 5X5 matrix

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    10

    Need help with determinant of 5X5 matrix

    I'm given his matrix and asked to find the determinant.

    \left[\begin{array}{ccccc}2&-2&0&0&-3\\3&0&3&2&-1\\0&1&-2&0&2\\-1&2&0&3&0\\0&4&1&0&0\end{array}\right]

    Now I do -4C_{3} + C_{2} \longrightarrow C_{2}which gives me this

    \left[\begin{array}{ccccc}2&-2&0&0&-3\\3&-12&3&2&-1\\0&9&-2&0&2\\-1&2&0&3&0\\0&0&1&0&0\end{array}\right]

    This eliminates the 5th row and 3rd column.

    I'm now left with this:

    \left[\begin{array}{cccc}2&-2&0&-3\\3&-12&2&-1\\0&9&0&2\\-1&2&3&0\end{array}\right]

    Now I'm trying to get rid of row and column 1:

    R_{1} + R{2} \longrightarrow R_{2}

    3R_{1} + 2R{4} \longrightarrow R_{4}

    \left[\begin{array}{cccc}2&0&0&0\\3&-9&2&7\\0&9&0&4\\-1&1&3&-3\end{array}\right]

    And now I'm left with this:

    \left[\begin{array}{ccc}-9&2&7\\9&0&4\\1&3&-3\end{array}\right]

    Now I can solve this and this is what I get:
    -9 \left[\begin{array}{cc}0&4\\3&-3\end{array}\right] -2 \left[\begin{array}{cc}9&4\\1&-3\end{array}\right] +7 \left[\begin{array}{cc}9&0\\1&3\end{array}\right]

    That gives me:

    2 [- 9(-12) - 2(-31) + 7(27)]= 2(359)

    This is where I don't understand because the answer in the book is 359, but what about the cofactor of 2 when I eliminated the row and column 1?

    Don't I have to multiply everything by 2 which would not be the answer in the book?

    Thank you.
    Last edited by Mrs. White; October 3rd 2009 at 10:26 AM. Reason: spelling
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by Mrs. White View Post
    I'm given his matrix and asked to find the determinant.

    \left[\begin{array}{ccccc}2&-2&0&0&-3\\3&0&3&2&-1\\0&1&-2&0&2\\-1&2&0&3&0\\0&4&1&0&0\end{array}\right]

    Now I do -4C_{3} + C_{2} \longrightarrow C_{2}which gives me this

    \left[\begin{array}{ccccc}2&-2&0&0&-3\\3&-12&3&2&-1\\0&9&-2&0&2\\-1&2&0&3&0\\0&0&1&0&0\end{array}\right]

    This eliminates the 5th row and 3rd column.

    I'm now left with this:

    \left[\begin{array}{cccc}2&-2&0&-3\\3&-12&2&-1\\0&9&0&2\\-1&2&3&0\end{array}\right]

    Now I'm trying to get rid of row and column 1:

    R_{1} + R{2} \longrightarrow R_{2}

    3R_{1} + 2R{4} \longrightarrow R_{4} Awkward says: here you doubled the determinant.

    \left[\begin{array}{cccc}2&0&0&0\\3&-9&2&7\\0&9&0&4\\-1&1&3&-3\end{array}\right]

    And now I'm left with this:

    \left[\begin{array}{ccc}-9&2&7\\9&0&4\\1&3&-3\end{array}\right]

    Now I can solve this and this is what I get:
    -9 \left[\begin{array}{cc}0&4\\3&-3\end{array}\right] -2 \left[\begin{array}{cc}9&4\\1&-3\end{array}\right] +7 \left[\begin{array}{cc}9&0\\1&3\end{array}\right]

    That gives me:

    2 [- 9(-12) - 2(-31) + 7(27)]= 2(359)

    This is where I don't understand because the answer in the book is 359, but what about the cofactor of 2 when I eliminated the row and column 1?

    Don't I have to multiply everything by 2 which would not be the answer in the book?

    Thank you.
    See above.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Derivative of a matrix inverse and matrix determinant
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2011, 09:18 AM
  2. Determinant of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: November 10th 2010, 10:07 PM
  3. Determinant of matrix
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 25th 2010, 07:35 PM
  4. Determinant of a 3X3 matrix
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 17th 2009, 06:01 AM
  5. Determinant of a 2 x 3 matrix?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 6th 2008, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum