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maggieL
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1) if A is a 3x3 matrix satisfying det(2AA^T)=8, then detA=±1
T or F?
 one year ago
 one year ago
maggieL Group Title
1) if A is a 3x3 matrix satisfying det(2AA^T)=8, then detA=±1 T or F?
 one year ago
 one year ago

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hartnn Group TitleBest ResponseYou've already chosen the best response.1
hi! still need help with this ?
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
yes please!
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
ok, we use the property that if there's a nXn matrix B, \(aB= a^nB\) which means if we take out the constant, it will be raised to n'th power
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so what about \(2AA^T=....?\)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
where ... is for determinant...
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
errr......
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
don't get it
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
here, since A is 3X3, n= 3 \(2AA^T=2^3AA^T\) from the property i mentioned....try to get this and ask doubts if any..
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
any more hints? I'm really bad at it:(
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
try to understand that step first...next step are very simple, only this first step is bummer
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
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 ?
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
yea this part I get. I don't get why the whole thing equals 8
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
that whole thing =8 is GIVEN part. we need to find whether det (A) = +/ 1 or not lets go to next steps, since \(XY=XY\) we will have \(2^3AA^T=8AA^T\) got this step too ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
lastly , determinant of any matrix is same as determinant of its transpose, \(so, A=A^T\) so, \(8AA=8 \implies A^2=1\) what can you say about det(A)from here ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
does det(A) = +1 or 1 ?
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
ohh I get it now! thanks! I got stuck in another T/F question if you don't mind helping as well?
 one year ago
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