- #1
bowlbase
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Homework Statement
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)
Homework Equations
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 doesn't 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.