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 + y + z = 5
x + 2y + 3z = 44
2x − y = −25
(xyz) = 
 
 
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

Here the matrix is {1,1,1,5; -1,2,3,44;2,-1,0,-25}

Eliminate the first column, so it becomes {1,0,0;1,3,-3;1,4,-2;5,49,-35}

Divide the second row by 3 and eliminate the second column to become {1,0,0; 0,1,0;-1/3,4/3,1;-34/3,49/3,7}

Lastly, Divide the third row by 2 and eliminate the third column, {1,0,0; 0,1,0; 0,0,1;-9,7,7}

Hence, {x,y,z}= {-9,7,7}

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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