A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
1) if A is a 3x3 matrix satisfying det(2AA^T)=8, then detA=±1
T or F?
anonymous
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1hi! still need help with this ?

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1so what about \(2AA^T=....?\)

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

hartnn
 3 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..

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

hartnn
 3 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
 3 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 ?

anonymous
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1does det(A) = +1 or 1 ?

anonymous
 3 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?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.