anonymous
  • anonymous
1) if A is a 3x3 matrix satisfying det(2AA^T)=8, then detA=±1 T or F?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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hartnn
  • hartnn
hi! still need help with this ?
anonymous
  • anonymous
yes please!
hartnn
  • hartnn
ok, we use the property that if there's a nXn matrix B, \(|aB|= a^n|B|\) which means if we take out the constant, it will be raised to n'th power

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hartnn
  • hartnn
so what about \(|2AA^T|=....?\)
hartnn
  • hartnn
where |...| is for determinant...
anonymous
  • anonymous
errr......
anonymous
  • anonymous
don't get it
hartnn
  • hartnn
here, since A is 3X3, n= 3 \(|2AA^T|=2^3|AA^T|\) from the property i mentioned....try to get this and ask doubts if any..
anonymous
  • anonymous
any more hints? I'm really bad at it:(
hartnn
  • hartnn
try to understand that step first...next step are very simple, only this first step is bummer
hartnn
  • hartnn
when i take constant out of the determinant (here, constant = 2) it gets raised to the power of 'n' where a matrix is of order nXn (here n=3) thats how we get 2^3 outside got this ?
anonymous
  • anonymous
yea this part I get. I don't get why the whole thing equals 8
hartnn
  • hartnn
that whole thing =8 is GIVEN part. we need to find whether det (A) = +/- 1 or not lets go to next steps, since \(|XY|=|X||Y|\) we will have \(2^3|AA^T|=8|A||A^T|\) got this step too ?
anonymous
  • anonymous
yepp
hartnn
  • hartnn
lastly , determinant of any matrix is same as determinant of its transpose, \(so, |A|=|A^T|\) so, \(8|A||A|=8 \implies |A|^2=1\) what can you say about det(A)from here ?
hartnn
  • hartnn
does det(A) = +1 or -1 ?
anonymous
  • anonymous
ohh I get it now! thanks! I got stuck in another T/F question if you don't mind helping as well?
hartnn
  • hartnn
sure :)
anonymous
  • anonymous
posted!

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