How do you solve using gaussian elimination or gauss-jordan elimination, $x + 2 y - z = - 5$ $x+2y-z=-5$ , $3 x + 2 y + 3 z = - 7$ $3x+2y+3z=-7$ , $5 x - y - 2 z = - 30$ $5x-y-2z=-30$ ?

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Answer 1 · 2016-05-14T05:37:25

$x = - 5$ $x=-5$
$y = 1$ $y=1$
$z = 2$ $z=2$

Gaussian Elimination or Gauss-Jordan elimination

$[(1,2,-1,|,-5),(3,2,3,|,-7),(5,-1,-2,|,-30)]$

$[(1,2,-1,|,-5),(0,-4,6,|,8),(0,-11,3,|,-5)]$

$[(1,2,-1,|,-5),(0,-2,3,|,4),(0,-11,3,|,-5)]$

$[(1,2,-1,|,-5),(0,-2,3,|,4),(0,-1,-12,|,-25)]$

$[(1,2,-1,|,-5),(0,1,39,|,79),(0,-1,-12,|,-25)]$

$[(1,0,-79,|,-163),(0,1,39,|,79),(0,0,27,|,54)]$

$[(1,0,0,|,-5),(0,1,0,|,1),(0,0,1,|,2)]$

$x=-5$
$y=1$
$z=2$

God bless....I hope the explanation is useful.

How do you solve using gaussian elimination or gauss-jordan elimination, x+2y-z=-5x+2y−z=−5x+2y-z=-5, 3x+2y+3z=-73x+2y+3z=−73x+2y+3z=-7, 5x-y-2z=-305x−y−2z=−305x-y-2z=-30?