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January 10th, 2014, 08:55 AM  #1 
Member Joined: Jan 2013 Posts: 96 Thanks: 0  Matrices
Find two 2x2 matrices with real entries A, B such that . (I need just an example.)

January 10th, 2014, 10:32 PM  #2  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Matrices Quote:
Well i played around with it for a while till i realized we could work with rows as one way to get an answer.  
January 11th, 2014, 09:10 AM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Matrices
Nice question with a nice solution!

January 11th, 2014, 11:22 AM  #4 
Member Joined: Jan 2013 Posts: 96 Thanks: 0  Re: Matrices
Thank you!

January 12th, 2014, 04:06 AM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Matrices
You're welcome. Just in case you haven't noticed , we now have an easy solution to an infinite amount of problems of this form. For IF THEN a solution will be We can also transpose both A , B and get another family of solutions. Then we would be working with columns. An interesting question to ask is 'what if ?' A place to start could be , Find a 2×2 matrix A such that Can it be found ? 
January 12th, 2014, 09:12 AM  #6 
Member Joined: Jan 2013 Posts: 96 Thanks: 0  Re: Matrices
Of course not, if A has real entries ( det(A)^2=1)!

January 12th, 2014, 09:39 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Matrices Quote:
 
January 12th, 2014, 09:42 AM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Matrices
Can we find A with complex entries? 
January 12th, 2014, 12:06 PM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Matrices Quote:
 
January 13th, 2014, 03:44 AM  #10 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Matrices
Find 4 distinct matrices A such that 

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