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Math Help - Need help with: Making a Matrix Singular and Finding Determinates

  1. #1
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    Need help with: Making a Matrix Singular and Finding Determinates

    Ok, i have been working on these problems for a bout an hour now and cant seem to find an answer.

    1.)

    Find all possible values of c that will make the matrix singluar

    (c-1) -2 -3
    (c-1) (c+1) -3
    0 0 1


    i used the formula (a11)(a22)(a33)-(a11)(a32)(a23)-(a12)(a21)(a33)+(a12)(a31)(a23)+(a13)(a21)(a32)-(a13)(a31)(a22)=0

    solved it out to get c^2+2c-3=0
    thus my roots are 3 and -1(but thats not the correct answer....)


    2.)

    Let A and B be 3X3 Matrices with det(A)=2 and det(B)=7

    i know that for det(AB) you multiply the 2 but i need to find

    det(2A)=?
    det(3AB)=?
    det(AB^-1)=?


    3.)

    If the determinate of a 4X4 matrix A is det(A)=9, and the matrix D is obtained from A by adding 3 times the third row to the second, determine det(D).



    Any help is greatly appreciated
    Thank you,
    Drew
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  2. #2
    A Plied Mathematician
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    Hmm. For 1.), I get the determinant to be

    1((c+1)(c-1)-(-2)(c-1))=c^{2}-1+2c-2=c^{2}+2c-3=0, the same as you. However, the solutions are c=1,-3, the opposite signs you got.

    For 2.), note that for an n\times n matrices A,B, and scalar a, you have

    \det(aA)=a^{n}\det(A),

    \det(AB)=\det(A)\,\det(B),

    and, if A is invertible, then

    \det(A^{-1})=\dfrac{1}{\det(A)}.

    That should enable you to compute all the required quantities.
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  3. #3
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    Thank you, Can anyone explain #3 for me please?
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  4. #4
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    Quote Originally Posted by Diggidy View Post
    [snip]
    3.)

    If the determinate of a 4X4 matrix A is det(A)=9, and the matrix D is obtained from A by adding 3 times the third row to the second, determine det(D).



    Any help is greatly appreciated
    Thank you,
    Drew
    There is a theorem you need to review regarding what happents to a determinant when you do this sort of elementary row operation. (Your class notes or textbook should list the various theorems for what happens to a determinant for diferent sorts of elementary row operations ....)
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