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

This Question is Closed

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1hi! still need help with this ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, 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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1where ... is for determinant...

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1here, 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..

maggieL
 2 years ago
Best ResponseYou've already chosen the best response.0any more hints? I'm really bad at it:(

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1try to understand that step first...next step are very simple, only this first step is bummer

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1when 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 ?

maggieL
 2 years ago
Best ResponseYou've already chosen the best response.0yea this part I get. I don't get why the whole thing equals 8

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1that 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 ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1lastly , 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 ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1does det(A) = +1 or 1 ?

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