Asked by Ciara

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

4x-y+3z = 12
x+4y+6z =-32
5x+3y+9z = 20
...... I NEED HELP WITH THE OTHER TWO PLEASE :)

4 -1 3 | 12

1 4 6 | -32

5 3 9 | 20

1 0 0 

0 1 0

0 0 1

4 -1 3 | 12

1 4 6 | -32 

5 3 9 | 20

4 -1 3 | 12 

4 16 24 | -128

5 3 9 | 20

4 -1 3 | 12

0 17 21 | -140

5 3 9 | 20

4 -1 3 | 12

0 17 21 | -140

20 12 36 | 80

4 -1 3 | 12

0 17 21 | -140

0 17 21 | 20

17y+21z = -140

17y+21z = 20
Answered by Damon



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



Step 1: Swap row 3 and 1


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



Step 2: Divide row 1 by 5


1 0.6 1.8 4
1 4 6 -32
4 -1 3 12



Step 3: Subtract row 1 from row 2


1 0.6 1.8 4
0 3.4 4.2 -36
4 -1 3 12



Step 4: Subtract (4 × row 1) from row 3


1 0.6 1.8 4
0 3.4 4.2 -36
0 -3.4 -4.2 -4



Step 5: Divide row 2 by 3.4


1 0.6 1.8 4
0 1 1.235 -10.588
0 -3.4 -4.2 -4



Step 6: Subtract (-3.4 × row 2) from row 3


1 0.6 1.8 4
0 1 1.235 -10.588
0 0 0 -40



Step 7: Divide row 3 by -40


1 0.6 1.8 4
0 1 1.235 -10.588
0 0 0 1



Matrix is now in row echelon form

Step 8: Subtract (4 × row 3) from row 1


1 0.6 1.8 0
0 1 1.235 -10.588
0 0 0 1



Step 9: Subtract (-10.588 × row 3) from row 2


1 0.6 1.8 0
0 1 1.235 0
0 0 0 1



Step 10: Subtract (0.6 × row 2) from row 1


1 0 1.059 0
0 1 1.235 0
0 0 0 1

Answered by Damon
http://www.idomaths.com/gauss_jordan.php

Answered by Ciara
Thats for x+4y+6z =-32 right ?
Answered by Damon
1 4 6 -32 yes

but your problem gives a very strange answer
Answered by Ciara
Okay for the 3rd one what am I supposed to put in the boxes ? what numbers ?
Answered by Damon
You can not reduce the last row to

0 0 1 something
Answered by Damon
You mean this ?
17y+21z = -140

that would be
0 17 21 -140
Answered by Ciara
Oh so for the last one I don't do anything ?
Answered by Ciara
No I was talking about this one 5x+3y+9z = 20
Answered by Ciara
4x-y+3z = 12
x+4y+6z =-32
5x+3y+9z = 20

We did the first two but not the last one
Answered by Damon
Huh,
they are
4 -1 3 12
1 4 6 -32
5 3 9 20

the trouble is that it can not be solved
Answered by Ciara
Okay thank you so much :)
Answered by Damon
calculate the determinant of the 3 by 3 on the left as if you were going to do Cramer rule
THE DETERMINANT IS ZERO
Answered by Ciara
Thank you !
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