How do you solve using gaussian elimination or gauss-jordan elimination, $2x–3y+2z=2$ , $x+4y-z=9$ , $-3x+y–5z=5$ ?

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Answer 1 · 2018-02-14T23:36:34

$x=115/31$ , $y=32/31$ and $z=-36/31$

Perform the Gauss Jordan elimination on the augmented matrix

$A=((2,-3,2,|,2),(1,4,-1,|,9),(-3,1,-5,|,5))$

I have written the equations not in the sequence as in the question in order to get $1$ as pivot.

Perform the folowing operations on the rows of the matrix

$R1larrR1-2R2$ ; $R3larrR3+3R2$

$A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,13,-16,|,32))$

$R3larr(R3+R1)$

$A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,2,-12,|,16))$

$R3larr(R3)/2$

$A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,1,-6,|,8))$

$R1larrR1+11R3; R2larrR2-4R3$

$A=((0,0,-62,|,72),(1,0,23,|,-23),(0,1,-6,|,8))$

$R1larr(R1)/(-62)$

$A=((0,0,1,|,-36/31),(1,0,23,|,-23),(0,1,-6,|,8))$

$R2larrR2-23R1; R3larrR3+6R1$

$A=((0,0,1,|,-36/31),(1,0,0,|,115/31),(0,1,0,|,32/31))$

Thus, $x=115/31$ , $y=32/31$ and $z=-36/31$

How do you solve using gaussian elimination or gauss-jordan elimination, 2x–3y+2z=22x–3y+2z=2, x+4y-z=9x+4y-z=9, -3x+y–5z=5-3x+y–5z=5?