Gauss-Jordan Method

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Guest

Guest
Hi,

I'm trying really hard to understand this using gauss jordan method with matrix. I understand the first step, but am confused with the additon. Can you please explain how how add, multiply and subtract to solve the problem below. Please list every step you take to solve the problem.


3x-4y = 1
5x + 2y = 19
 
Gauss-Jordan is something that gets easier with practice.

Your goal is to get the matrix into the form:

1 0 x
0 1 y

Let's step through yours. R1 means row 1 and R2 means row 2.

3 -4 1
5 2 19


(1/3) times R1 -->R1:

1 -4/3 1/3
5 2 19


-5 times R1 plus R2-->R2:

1 -4/3 1/3
0 26/3 52/3


3/26 times R2-->R2:

1 -4/3 1/3
0 1 2


4/3 times R2 plus R1-->R1:

1 0 3
0 1 2

There you have it:

x=3 and y=2


Do you see now what the goal is?. It's a process of elimination.
 
I deeply appreciate your help. How did you get 26/3..that is what confusing!
 
using the previous reply

1 -4/3 1/3
5 2 19


-5 times R1 plus R2-->R2:

1 -4/3 1/3
0 26/3 52/3


expanding the 26/3 for you...

-5 x (-4/3) + 2

=(20/3) + 2

= (20/3) +(6/3)

=26/3
 
As the tutor mentioned, he was converting to thirds.

2 = 2/1 = 6/3.

Eliz.
 
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