September 26th, 2012, 06:49 AM  #1 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  unique solution
Does the matrix 0 1 0 15 0 0 1 7 has a unique solution? Thank you in advance 
September 26th, 2012, 08:32 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: unique solution Hello, shine123! Quote: With three unknowns and only two equations, the answer is NO.  
September 26th, 2012, 10:21 AM  #3 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  Re: unique solution
So, does in this case the first (left) unknown is a parameter?

September 27th, 2012, 07:25 AM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: unique solution
I assume you are asking if the system of equation reducing to this augmented matrix has a unique solution. It should be easy to see that this matrix is equivalent to the system of equations 0x+ 1y+ 0x= 15 and 0x+ 0y+ 1z= 7, which are simply y= 15 and z= 7. x can be any number. IF that is what you mean by "the first (left) unknown is a parameter?", yes. The solution set is (x, y, z)= (t, 15, 7) where t can be any number.

September 28th, 2012, 08:00 AM  #5 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  Re: unique solution
THANK YOU!!!!


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