How do you solve using gaussian elimination or gauss-jordan elimination, $x + y + z = 2$ $x+y+z=2$ , $2 x - 3 y + z = - 11$ $2x-3y+z=-11$ , $- x + 2 y - z = 8$ $-x+2y-z=8$ ?

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Answer 1 · 2018-06-01T16:52:12

The solution is $((x),(y),(z))=((1/3),(10/3),(-5/3))$

The augmented matrix is

$A=((1,1,1,|,2),(2,-3,1,|,-11),(-1,2,-1,|,8))$

The pivot is in the the first column of the first row

Perform the operations on the rows

$R2larrR2-2R1$ and $R3larrR3+R1$

$=>$ , $((1,1,1,|,2),(0,-5,-1,|,-15),(0,3,0,|,10))$

Make the pivot in the second column

$R2larr(R2)/(-5)$

$=>$ , $((1,1,1,|,2),(0,1,1/5,|,3),(0,3,0,|,10))$

Eliminate the second column

$R1larrR1-R2$ and $R3larrR3-3R2$

$=>$ , $((1,0,4/5,|,-1),(0,1,1/5,|,3),(0,0,-3/5,|,1))$

Make the pivot in the third column

$R3larr(R3xx-5/3)$

$=>$ , $((1,0,4/5,|,-1),(0,1,1/5,|,3),(0,0,1,|,-5/3))$

Eliminate the third column

$R1larr(R1-4/5xxR3)$ and $R2larr(R2-1/5xxR3)$

$=>$ , $((1,0,0,|,1/3),(0,1,0,|,10/3),(0,0,1,|,-5/3))$

The solution is

$((x),(y),(z))=((1/3),(10/3),(-5/3))$

How do you solve using gaussian elimination or gauss-jordan elimination, x+y+z=2x+y+z=2x+y+z=2, 2x-3y+z=-112x−3y+z=−112x-3y+z=-11, -x+2y-z=8−x+2y−z=8-x+2y-z=8?