Thread: gauss-jordan elimination

I have two problems I need help with.

1.

[2 1 -1 3 l 0]
[3 -2 1 -4 l -24]
[1 1 -1 1 l 2]
[1 -1 2 -5 l -16]

2.
[1 -1 1 -1 l 4]
[1 2 1 1 l 2]
[2 3 4 5 l 5]
[3 4 2 -1 l 8]

Can you help me with this question. Also, please show the steps to how you got your answer. Thanks!

Originally Posted by starrynight

[2 1 -1 3 l 0]
[3 -2 1 -4 l -24]

Do you realise that the above possibly come from:
2a + b - c + 3d = 0
3a - 2b + c - 4d = -24
?

How far can you get on your own?

Hi Wilmer,
It is supposed to be a 5 by 4 matrix. Then i am supposed to get the matrix to have a diagonal row of ones. The only problem is that i am not sure how many zeros it is supposed to have. (The letters stand for numbers that we do not know yet)

Is it supposed to look like this:

[1 0 0 0 l a]
[0 1 0 0 l b]
[0 0 1 0 l c]
[0 0 0 1 l d]

OR

Is it supposed to be like this:

[1 a b c l d]
[0 1 e f l g]
[0 0 1 h l i]
[0 0 0 1 l j]

NO. I think you need help from your math teacher.

This matrix:
[2 1 -1 3 l 0]
[3 -2 1 -4 l -24]
[1 1 -1 1 l 2]
[1 -1 2 -5 l -16]
was obtained from 4 equations, each with 4 variables;
if we let these variables be a,b,c,d then:

[2 1 -1 3 l 0] : 2a + b - c + 3d = 0
[3 -2 1 -4 l -24] : 3a - 2b + c - 4d = -24
[1 1 -1 1 l 2] : a + b - c + d = 2
[1 -1 2 -5 l -16] : a - b + 2c - 5d = -16

There are various ways to solve these;
the gauss-jordan elimination using a matrix is one of them.

But that's near impossible to "teach" here...

Try learning by yourself; go here:
http://sks99.com/ch9/gauss.htm