SOLUTION: how do u solve these linear systems by gauss elimination or any other method? x -5y +0z +10w= 27 5x -25y +10z -4w= -47 10x +2y -1z +4w= 36 2x +4y -2z +0w= 12

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: how do u solve these linear systems by gauss elimination or any other method? x -5y +0z +10w= 27 5x -25y +10z -4w= -47 10x +2y -1z +4w= 36 2x +4y -2z +0w= 12       Log On

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Question 5154: how do u solve these linear systems by gauss elimination or any other method?
x -5y +0z +10w= 27
5x -25y +10z -4w= -47
10x +2y -1z +4w= 36
2x +4y -2z +0w= 12

Thank you very much I appreciate your help.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
user Cramer's rule --> but that will involve you calculating 4x4 determinants, so you may decide to ignore that method :-)

Gaussian elimination... here goes :-(

matrix+%285%2C+4%2C+%0D%0A+1%2C++-5%2C++0%2C+10%2C++27%2C%0D%0A+5%2C+-25%2C+10%2C+-4%2C+-47%2C%0D%0A10%2C+++2%2C+-1%2C++4%2C++36%2C%0D%0A+2%2C+++4%2C+-2%2C++0%2C++12%29%0D%0A

matrix+%285%2C+4%2C+%0D%0A+1%2C++-5%2C++0%2C++10%2C+++27%2C%0D%0A+0%2C+++0%2C+10%2C+-54%2C+-182%2C%0D%0A+0%2C++52%2C+-1%2C+-96%2C+-234%2C%0D%0A+0%2C++14%2C+-2%2C+-20%2C++-42%29%0D%0A

re-arrnage the rows to move the zero further down and get the smallest number (the 14) in the correct place

matrix+%285%2C+4%2C+%0D%0A+1%2C++-5%2C++0%2C++10%2C+++27%2C%0D%0A+0%2C++14%2C+-2%2C+-20%2C++-42%2C%0D%0A+0%2C+++0%2C+10%2C+-54%2C+-182%2C%0D%0A+0%2C++52%2C+-1%2C+-96%2C+-234%29%0D%0A

divide second by 14 to get a 1

matrix+%285%2C+4%2C+%0D%0A+1%2C++-5%2C++0%2C++10%2C+++27%2C%0D%0A+0%2C+++1%2C+-1%2F7%2C+-10%2F7%2C++-3%2C%0D%0A+0%2C+++0%2C+10%2C+-54%2C+-182%2C%0D%0A+0%2C++52%2C+-1%2C+-96%2C+-234%29%0D%0A

matrix+%285%2C+4%2C+%0D%0A+1%2C+-5%2C++++0%2C+++++10%2C+++27%2C%0D%0A+0%2C++1%2C+-1%2F7%2C++-10%2F7%2C+++-3%2C%0D%0A+0%2C++0%2C+++10%2C++++-54%2C+-182%2C%0D%0A+0%2C++0%2C+45%2F7%2C+-152%2F7%2C++-78%29%0D%0A

divide by 10 to get a 1

matrix+%285%2C+4%2C+%0D%0A+1%2C+-5%2C++++0%2C+++++10%2C+++27%2C%0D%0A+0%2C++1%2C+-1%2F7%2C++-10%2F7%2C+++-3%2C%0D%0A+0%2C++0%2C++++1%2C++++-27%2F5%2C+-91%2F5%2C%0D%0A+0%2C++0%2C+45%2F7%2C+-152%2F7%2C++-78%29%0D%0A

matrix+%285%2C+4%2C+%0D%0A+1%2C+-5%2C++++0%2C+++++10%2C+++27%2C%0D%0A+0%2C++1%2C+-1%2F7%2C++-10%2F7%2C+++-3%2C%0D%0A+0%2C++0%2C++++1%2C++++-27%2F5%2C+-91%2F5%2C%0D%0A+0%2C++0%2C++++0%2C+++++13%2C++39%29%0D%0A

so, 13w = 39 --> w=3
z - 81/5 = -91/5 --> z = -2
y + 2/7 - 30/7 = -3 --> y = 1
x - 5 + 30 = 27 --> x = 2

THEN IMPORTANTLY, you need to put these 4 answers into each of the original 4 equations to check...check with the 4th one first --> if that works, then odds on you are correct.

PS i hate Gaussian Elimination!

jon