How do you solve using gaussian elimination or gauss-jordan elimination, $3x – y + 2z = 6$ , $-x + y = 2$ , $x – 2z = -5$ ?

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Answer 1 · 2016-07-16T07:00:52

$color(red)(x=1,y=3,z=3)$

Initial Augmented Matrix:

$[ ( 3, -1, 2, 6), ( -1, 1, 0, 2), ( 1, 0, -2, -5) ]$

Adding Row-2 and Row-3 to Row-1

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

Dividing Row-1 by 3

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

Adding Row-1 to Row-2

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

Adding Row-1 from Row-3

$[ ( 1, 0, 0, 1), ( 0, 1, 0, 3), ( 0, 0, -2, -6) ]$

Dividing Row-3 by -2

$[ ( 1, 0, 0, 1), ( 0, 1, 0, 3), ( 0, 0, 1, 3) ]$

Obviously

$color(red)(x=1,y=3,z=3)$

How do you solve using gaussian elimination or gauss-jordan elimination, 3x – y + 2z = 63x – y + 2z = 6, -x + y = 2-x + y = 2, x – 2z = -5x – 2z = -5?