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Question 395394: I could definitely use help with the following: Solve the following system of equations using matrices and guassian or gauss-jordan elimination. Here is the system of equations:
3a+b-c=0
2a+3b-5c=1
a-2b+3c=-4
My augmented matrix is:
3 1 -1 0
2 3 -5 1
1 -2 3 -4
I swapped R3 and R1->R1
1 -2 3 -4
2 3 -5 1
3 1 -1 0
Now I'm stuck. Could a tutor please help? Thank you very much!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Here is the system of equations:
3a+b-c=0
2a+3b-5c=1
a-2b+3c=-4
My augmented matrix is:
3 1 -1 0
2 3 -5 1
1 -2 3 -4
I swapped R3 and R1->R1
1 -2 3 -4
2 3 -5 1
3 1 -1 0
---------------------
Add -2 times R1 to R2
Add -3 times R1 to R3
--------
1 -2 3 -4
0 7 -11 9
0 7 -10 12
------------
Subtract R2 from R3
---
1 -2 3 -4
0 7 -11 9
0 0 1 3
------------
z = 3
---
Substitute into R2 to solve for "y":
7y -11*3 = 9
7y = 42
y = 6
---
Substitute into$1 to solve for "x":
x -2*6+3*3 = -4
x -12+9 = -4
x-3= -4
x = -1
-----
Solution: (-1,6,3)
========================
Cheers,
Stan H.
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