Results 1 to 4 of 4

Math Help - Linear Algebra: Finding Determinant Using the Cramer's Ruler

  1. #1
    Junior Member
    Joined
    May 2007
    Posts
    69

    Linear Algebra: Finding Determinant Using the Cramer's Ruler

    Hello, I have a homework problem that I am not seeing quite well. Please help somebody.

    1) Let A be a 4 by 4 matrix. If

    adjoint A=
    2 0 0 0
    0 2 1 0
    0 4 3 2
    0 -2 -1 2

    find A.

    Answer from back of the book:

    A=
    1 0 0 0
    0 4 -1 1
    0 -6 2 -2
    0 1 0 1

    *I have no clue on how to go from Adjoint A to A.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,841
    Thanks
    320
    Awards
    1
    Quote Originally Posted by googoogaga View Post
    Hello, I have a homework problem that I am not seeing quite well. Please help somebody.

    1) Let A be a 4 by 4 matrix. If

    adjoint A=
    2 0 0 0
    0 2 1 0
    0 4 3 2
    0 -2 -1 2

    find A.

    Answer from back of the book:

    A=
    1 0 0 0
    0 4 -1 1
    0 -6 2 -2
    0 1 0 1

    *I have no clue on how to go from Adjoint A to A.
    You may find this site helpful.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2007
    Posts
    69
    I still don't understand because the matrix in the site is a 3 by 3 matrix. I just can't see it. Please I would like to see the steps. thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,841
    Thanks
    320
    Awards
    1
    Quote Originally Posted by googoogaga View Post
    adjoint A=
    2 0 0 0
    0 2 1 0
    0 4 3 2
    0 -2 -1 2
    I believe that the adjoint of A is equal to A. So find the adjoint of the adjoint.

    You have to create a 4 x 4 matrix using the cofactor determinants. So
    A_{11} = \left | \begin{matrix} 2 & 1 & 0 \\ 4 & 3 & 2 \\ -2 & -1 & 2 \end{matrix} \right | = 4

    Then do the same for the other 15 cofactors determinants, then take the transpose of the resulting matrix. The website says that this is the adjoint, which I'll let you verify for yourself.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 1st 2011, 10:00 PM
  2. Replies: 3
    Last Post: January 30th 2010, 10:23 PM
  3. Linear Algebra: Determinant question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 25th 2008, 02:18 AM
  4. Determinant - Linear Algebra
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 23rd 2007, 04:46 PM
  5. [SOLVED] Need help finding a preimage (linear algebra)
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 20th 2006, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum