SOLUTION: Use the gauss-jordan method to solve this system of equation 4x + 4y - 4z = 24 2x - y + z = -9 x - 2y + 3z = 1 can you show me step by step how to solve this problem? Dia

Algebra ->  College  -> Linear Algebra -> SOLUTION: Use the gauss-jordan method to solve this system of equation 4x + 4y - 4z = 24 2x - y + z = -9 x - 2y + 3z = 1 can you show me step by step how to solve this problem? Dia      Log On


   

Question 499212: Use the gauss-jordan method to solve this system of equation
4x + 4y - 4z = 24
2x - y + z = -9
x - 2y + 3z = 1
can you show me step by step how to solve this problem?
Diana
Found 2 solutions by Alan3354, emargo19:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
http://www.youtube.com/watch?v=CsTOUbeMPUo
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this is covered in great detail in many places.

Answer by emargo19(101) About Me  (Show Source):
You can put this solution on YOUR website!
4x+%2B+4y+-+4z+=+24 (eq1)
2x+-++y+%2B+z++=+-9 (eq2) multiply by -2

4x+%2B+4y+-+4z+=+24
-4x+%2B+2y+-+2z++=18
---------------------
6y+-+6z+=+42 (new eq)


4x+%2B+4y+-+4z+=+24 (eq1)
x++-+2y+%2B+3z+=+1 (eq3) multiply by -4

So
+4x+%2B+4y+-+4z+=+24
-4x+%2B+8y+-+12z+=-4
----------------------
0+++%2B+12y-+16z+=20 (New eq)

**Next use both new equations **
6y+-+6z+=+42 multiply by -2
12y+-16z=+20
gives these
-12y+%2B+12z+=+-84
12y++-+16z+=++20
---------------------
0++++-+4z++=+-64
++++++++z++=++16

Substitute z=16 in eq 6y-6z=42
6y-6%2816%29=42
6y-96=42
6y=138
y=23

substitute y=23 and z=16 in equation 1.
4x+%2B+4y+-+4z+=+24
4x%2B4%2823%29-+4%2816%29=24
4x%2B92-64=24
4x=-4
x=-1

Solution:(-1,23,16)