SOLUTION: Using the Gauss-Jordan elimination method, solve the following linear system. You can use a calculator or Excel Minverse, Mmult to get your answer - 10 x + 14 y + 3 z = 74 +

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Using the Gauss-Jordan elimination method, solve the following linear system. You can use a calculator or Excel Minverse, Mmult to get your answer - 10 x + 14 y + 3 z = 74 +      Log On


   

Question 298763: Using the Gauss-Jordan elimination method, solve the following linear system.
You can use a calculator or Excel Minverse, Mmult to get your answer
- 10 x + 14 y + 3 z = 74
+ x + 17 y + 9 z = 85
- 13 x - 8 y + 3 z = 14
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
system%28-10x%2B14y%2B3z=74%2C%0D%0Ax%2B17y%2B9z+=+85%2C%0D%0A-13x-8y%2B3z=14%29
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Put all those red numbers in a 3x4 augmented matrix
like this:



On your TI-83 or TI-84,

Press CLEAR

Press 2ND
Press x-1 (MATRIX)
Prees the right arrow twice to highlight EDIT
Press ENTER
Press 3
Press ENTER
Press 4
Press ENTER
Type -10, 
Press ENTER
Type 14,
Press ENTER
Type 3,
Press ENTER
Type 74
Press ENTER
Type 1
Press ENTER
...
continue typing in all the rest of the elements 
in the matrix, pressing ENTER after each. Then
...
Press 2ND
Press MODE (QUIT)
Press 2ND
Press x-1 (MATRIX)
Press right arrow to highlight MATH
Press up arrow 5 times to highlight B:rref(
Press ENTER  you should see rref( on the screen
Press 2nd
Press x-1 (MATRIX)
Press ENTER  you should see rref([A]
Press ENTER

You should see  

rref([A]
    [[1 0 0 -2]
     [0 1 0 3 ]
     [0 0 1 4 ]]

Interpret this as the system:

system%281x%2B0y%2B0z=-2%2C0x%2B1y%2B1z=3%2C+0x%2B0y%2B1z=4%29

or

system%28x=-2%2Cy=3%2Cz=4%29  
Edwin