How do you solve using gaussian elimination or gauss-jordan elimination, $2 x - 3 y - 2 z = 10$ $2x-3y-2z=10$ , $3 x - 2 y + 2 z = 0$ $3x-2y+2z=0$ , $4 z - y + 3 z = - 1$ $4z-y+3z=-1$ ?

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Answer 1 · 2018-01-09T17:03:50

$x = 2$ $x=2$ , $y = 0$ $y=0$ and $z = - 3$ $z=-3$

Perform the Gauss Jordan elimination on the augmented matrix

$A=((2,-3,-2,|,10),(3,-2,2,|,0),(4,-1,3,|,-1))$

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

$R1larrR1+R2$

$A=((5,-5,0,|,10),(3,-2,2,|,0),(4,-1,3,|,-1))$

$R1larr(R1)/5$

$A=((1,-1,0,|,2),(3,-2,2,|,0),(4,-1,3,|,-1))$

$R2larrR2-3R1$ ; $R3larrR3-4R1$

$A=((1,-1,0,|,2),(0,1,2,|,-6),(0,3,3,|,-9))$

$R3larrR3-3R2$

$A=((1,-1,0,|,2),(0,1,2,|,-6),(0,0,-3,|,9))$

$R3larrR3/(-3)$

$A=((1,-1,0,|,2),(0,1,2,|,-6),(0,0,1,|,-3))$

$R2larrR2-2R3$

$A=((1,-1,0,|,2),(0,1,0,|,0),(0,0,1,|,-3))$

$R1larrR1+R2$

$A=((1,0,0,|,2),(0,1,0,|,0),(0,0,1,|,-3))$

Thus $x=2$ , $y=0$ and $z=-3$

How do you solve using gaussian elimination or gauss-jordan elimination, 2x-3y-2z=102x−3y−2z=10 2x-3y-2z=10, 3x-2y+2z=03x−2y+2z=03x-2y+2z=0, 4z-y+3z=-14z−y+3z=−14z-y+3z=-1?