How do you solve using gaussian elimination or gauss-jordan elimination, $x + y - 5 z = - 13$ $x+y-5z=-13$ , $3 x - 3 y + 4 z = 11$ $3x-3y+4z=11$ , $x + 3 y - 2 z = - 11$ $x+3y-2z=-11$ ?

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Answer 1 · 2016-04-06T19:17:07

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

Initial Augmented Matrix:
$( (1, 1, -5, -13), ( 3, -3, 4, 11), ( 1, 3, -2, -11) )$

Using row 1 as pivot row and column 1 as pivot column
Non-pivot rows reduced for pivot column
$( ( 1, 1, -5, -13), ( 0, -6, 19, 50), ( 0, 2, 3, 2) )$

Using row 2 as pivot row
pivot row reduced:
$( ( 1, 1, -5, -13), ( 0, 1, -3.17, -8.33), ( 0, 2, 3, 2) )$

Non-pivot rows reduced for pivot column
$( ( 1, 0, -1.83, -4.67), ( 0, 1, -3.17, -8.33), ( 0, 0, 9.33, 18.67) )$

Using row 3 as pivot row
pivot row reduced:
$( ( 1, 0, -1.83, -4.67), ( 0, 1, -3.17, -8.33), ( 0, 0, 1, 2) )$

Non-pivot rows reduced for pivot column
$( ( 1, 0, 0, -1), ( 0, 1, 0, -2), ( 0, 0, 1, 2) )$

How do you solve using gaussian elimination or gauss-jordan elimination, x+y-5z=-13x+y−5z=−13x+y-5z=-13, 3x-3y+4z=113x−3y+4z=113x-3y+4z=11, x+3y-2z=-11x+3y−2z=−11x+3y-2z=-11?