My Math Forum unique solution

 Linear Algebra Linear Algebra Math Forum

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

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!!!!

 Tags solution, unique

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mathmari Applied Math 2 April 11th, 2013 01:36 PM sab456 Number Theory 2 November 13th, 2012 09:58 PM aaron-math Linear Algebra 1 September 30th, 2011 02:33 PM imbored Real Analysis 0 February 23rd, 2010 09:49 PM imbored Applied Math 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top