My Math Forum echelon method expressing with infinite solutions
 User Name Remember Me? Password

 Linear Algebra Linear Algebra Math Forum

 August 29th, 2016, 03:46 PM #1 Member   Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2 echelon method expressing with infinite solutions Hi, Can someone explain to me how you express the answer for using the echelon method when there are an infinite number of solutions? For example, if you have a matrix of: 1 2 l 3 0 0 l 0 How do I express the answer? For my homework, it has to be ( , y) but I have no idea what goes in the first part and there is not a single example in my book of how to express it. Last edited by blimper; August 29th, 2016 at 03:54 PM.
 August 29th, 2016, 04:06 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,382 Thanks: 1281 $(1,2)\cdot (x,y) = 3$ $x + 2y = 3$ $y = \dfrac{3-x}{2}$ so all vectors $c\begin{pmatrix}x \\ \dfrac {3-x}{2}\end{pmatrix},~c \in \mathbb{R}$ are solutions Thanks from topsquark
 August 29th, 2016, 04:31 PM #3 Member   Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2 I guess what i was thinking is if I had something like: 1 -5/6 l -1/6 0 0 l 0 It would become: x-5/6y= -1/6 leading to x = 5y-1/6 Where my answer would be 5y-1 ( -----, y ) 6 (Is there a tutorial for how to express things on here like you did?)
August 29th, 2016, 04:48 PM   #4
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,382
Thanks: 1281

Quote:
 Originally Posted by blimper I guess what i was thinking is if I had something like: 1 -5/6 l -1/6 0 0 l 0 It would become: x-5/6y= -1/6 leading to x = 5y-1/6 Where my answer would be 5y-1 ( -----, y ) 6 (Is there a tutorial for how to express things on here like you did?)
that's equally valid though generally you want to use the first vector element as the independent variable. I would do this example as

$x - \dfrac 5 6 y = -\dfrac 1 6$

$6x -5y = 1$

$y = \dfrac {6x-1}{5}$

so all vectors

$c \begin{pmatrix} x \\ \frac{6x-1}{5}\end{pmatrix},~c \in \mathbb{R}$

 August 30th, 2016, 06:53 PM #5 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 1 2 1 3 0 0 1 0 is the matrix of the system of equations x+2y+z=3 0x+0y+z=0 in augmented form. In rref, by elementary row operations which don't change the solution, the matrix is 1 2 0 3 0 0 1 0 from which z=0, x+2y=3 y is arbitrary and x=3-2y

 Tags echelon, expressing, infinite, method, solutions

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post 84grandmarquis Linear Algebra 2 September 29th, 2013 01:59 PM EduXx Computer Science 2 October 7th, 2012 03:10 PM niaboc Algebra 3 October 1st, 2012 03:36 PM ansar Linear Algebra 0 October 19th, 2011 02:39 AM 84grandmarquis Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top