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Multipying Determinants

  1. Nov 1, 2013 #1
    1. The problem statement, all variables and given/known data
    This is a practice problem where the solutions are given.
    Both are 3x3 matrices.

    det A=-2 and det B=1
    find the following:
    1)det(A6)
    2) det(B-1A3B3AT)
    3) det(4(AT)2(B-1)4)
    4) det((2BT)-1)

    2. Relevant equations



    3. The attempt at a solution
    I get the first two easily enough, 64 and 16. However, I'm not getting anything near the 256 and 1/8 (answers in order).

    I guess it is the multiples of 4 and 2 that are screwing me up. I know that det AT=det A and det A-1=det ##\frac{1}{A}##

    I thought maybe making two matrices such that the diagonals multiply to -2 and 1 respectively. So, 1*1*-2 and 1*1*1. Then multiplying each row by 4. Then: 4*4*-8 and 4*4*4.

    So the new det would be A=128 and B=64. And then placing them back in the 3rd equation but this clearly doesnt work as 644 is much greater than 1282.

    However, if I left it as 1282 divided by 64 then I get the correct answer. I don't know if this is a fluke or not but it seems to me that not taking 64 to the 4th power is counter to the equation.

    thanks for the help.
     
  2. jcsd
  3. Nov 1, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    If A is an nxn matrix and c is a constant, then det(cA)=c^n*det(A).
     
  4. Nov 1, 2013 #3
    Thank you so much! I guess we hadn't covered that yet.
     
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