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

This Question is Closed

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

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

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

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

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

maggieL
 one year 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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