Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.

Question

4x-y+3z = 12
x+4y+6z =-32
5x+3y+9z = 20

Answer 1

Enter your coefficients here and see all the details:

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

Answer 2

I don't know how to use that

Answer 3

When I do it , it says Im wrong

Answer 4

well, when I do it, it says I'm right, so why don't you show your work here and we can see how things go?

Answer 5

How did you do it ? what do you put in the boxes ?

Answer 6

I actually have to show my work , But I need help with this

Answer 7

I'll get you started. But you clearly need to study the examples in your text. Or, just do a google and you will find lots of examples online.

You start with your matrix of coefficients:

4 -1 3 | 12
1 4 6 | -32
5 3 9 | 20

You want to work things so that you have a final matrix with the left side looking like

1 0 0
0 1 0
0 0 1

And then the 4th column will have the values of the variables.

So, starting with

4 -1 3 | 12
1 4 6 | -32
5 3 9 | 20

if you multiply the 2nd row by 4 you have

4 -1 3 | 12
4 16 24 | -128
5 3 9 | 20

Now if you subtract the top row from the 2nd row, you have

4 -1 3 | 12
0 17 21 | -140
5 3 9 | 20

Now multiply the 3rd row by 4 and you have

4 -1 3 | 12
0 17 21 | -140
20 12 36 | 80

Now subtract the top row from the 3rd row and you have

4 -1 3 | 12
0 17 21 | -140
0 17 21 | 20

Woah! At this point you have

17y+21z = -140
17y+21z = 20

so there is no solution, since -140 ≠ 20

You really should go back to the web site and play around with some numbers just to get used to how it works.