SOLUTION: Please help me solve this system of equations using the Gauss-Jordan method. 4x - 3y +z +w = 21 -2x - y + 2z + 7w = 2 10x - 5z - 20w = 15

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help me solve this system of equations using the Gauss-Jordan method. 4x - 3y +z +w = 21 -2x - y + 2z + 7w = 2 10x - 5z - 20w = 15      Log On


   

Question 315481: Please help me solve this system of equations using the Gauss-Jordan method.

4x - 3y +z +w = 21
-2x - y + 2z + 7w = 2
10x - 5z - 20w = 15
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


Write the augmented matrix:


1*R1+2*R2->R2



-5*R1+2*R3->R3



-1%2F5*R2->R2
1%2F15*R3->R3



 3*R2+1*R1->R1
-1*R2+1*R3->R3



1%2F4*R1->R1



Write as a system of equations:



Simplify

system%28x+-%281%2F2%29z+-2w+=+3%2F2%2C%0D%0A++y+-+z+-+3w+=+-5%29

Solve only for the first two variables, since there are
only two equations:

system%28x+=+3%2F2+%2B%281%2F2%29z%2B2w%2C%0D%0A++y+=+-5%2Bz%2B3w%29

Let z be arbitrary variable a and let w be arbitrary variable b

system%28x+=+3%2F2+%2B%281%2F2%29a%2B2b%2C%0D%0A++y+=+-5%2Ba%2B3b%2Cz=a%2Cw=b%29 

or

(x, y, z, w) = (3%2F2%2B%281%2F2%29a%2B2b,-5+a+3b,a,b)

Edwin