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 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
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Joined: Dec 2006
From: Lexington, MA

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Re: unique solution

Hello, shine123!

Quote:
 $\text{Does the matrix }\,\left[\begin{array}{ccc|c} 0&1&0&-15 \\ \\ \\ 0&0&1&7\end{array}\right]\,\text{ have a unique solution?}$

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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