SOLUTION: I am so confused as to how to figured out a matrix problem using the Gauss-Jordan Method. Problem: 3X-2Y=-8Z+9 -2X+Z=-2Y+3 2Y-3Z+X=8 Thanks!!!!

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Question 29946: I am so confused as to how to figured out a matrix problem using the Gauss-Jordan Method.
Problem:
3X-2Y=-8Z+9
-2X+Z=-2Y+3
2Y-3Z+X=8
Thanks!!!!
Answer by brianunlv(12) (Show Source):
You can put this solution on YOUR website!
system of equations we have:
+3x - 2y + 8z = 9
-2x + 2y + z = 3
+x + 2y - 37 = 8
in equation form:
-
|3 -2 8 |x|`|9|
|-2 2 1 |y|=|3|
|1 2 -3 |z|`|8|
-
in matrix form:
-
|3 -2 8 |9||x|
|-2 2 1 |3||y|
|1 2 -3 |8||z|
-
first do gauss elemination (bottum left triangle = 0):
1.switch row1(R1) with row3(R3):
-
|1 2 -3 |8||x|
|-2 2 1 |3||y|
|3 -2 8 |9||z|
-
2.subtract 3*(R1) from (R3):
-
|1 2 -3 |8||x|
|-2 2 1 |3||y|
|0 -8 17 |-15||z|
-
3.subtract -4*(R1) from (R3):
-
|1 2 -3 |8||x|
|-2 2 1 |3||y|
|0 0 5 |9||z|--->we can see z = 9/5 already
-
4.subtract -2*(R1) from (R2):
-
|1 2 -3 |8||x|
|0 6 -5 |19||y|
|0 0 5 |9||z|
-
Now do jordan elemination (top right triangle = 0):
1. subtract -5/3*(R1) from (R2):
-
|1 2 -3 |8||x|
|0 6 0 |97/3||y|--->we can see y = (97/3)/6 already
|0 0 5 |9||z|
-
2. So we can now find x with back substitution:
x + 2((97/3)/6) - 3(9/5) = 8
x + (1164/3) - (27/5) = 8
x + 382 3/5 = 8
x = 8 - 382 3/5
x = 374 3/5
Regards,
Brian Bird