The system of linear equations has a unique solution. Find the solution using Ga

Algebra
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The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

 
x + 2y − z = −10
x + z = 0
2x − y − z = −15
(xyz) = 
  
Apr 21st, 2015

subtract the first equation from the second one, then divide the second equation by -2; subtract the first equation multiplied by 2 from the third one:

x + 2y  -   z   = -10

        y   -  z   =  -5

    -5y  +   z    =  5

add the second equation multiplied by 5 to the third equation:

x + 2y  -   z   =  - 10

        y   -  z   =    -5

             - 4z  =  - 20

Then from the last equation z = -20/-4 = 5, from the second equation y = z -5 = 0, from the first equation 

x = -2y + z - 10 = 0 + 5 - 10 = - 5

Answer: (-5, 0, 5). 


Apr 21st, 2015

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Apr 21st, 2015
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