How do you solve using gaussian elimination or gauss-jordan elimination, $x + 2 y + 2 z = 9$ $x+2y+2z=9$ , $x + y + z = 9$ $x+y+z=9$ , $3 x - y + 3 z = 10$ $3x-y+3z=10$ ?

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Answer 1 · 2018-04-06T15:10:38

$x = 9$ $x=9$ , $y = \frac{17}{4}$ $y=17/4$ and $z = - \frac{17}{4}$ $z=-17/4$

Perform the Gauss Jordan elimination on the augmented matrix

$A=((1,2,2,|,9),(1,1,1,|,9),(3,-1,3,|,10))$

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

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

$A=((1,2,2,|,9),(0,-1,-1,|,0),(0,-7,-3,|,-17))$

$R1larrR1+2R2$ ; $R3larrR3-7R2$

$A=((1,0,0,|,9),(0,-1,-1,|,0),(0,0,4,|,-17))$

$R2larrR2+1/4R3$

$A=((1,0,0,|,9),(0,-1,0,|,-17/4),(0,0,4,|,-17))$

$R2larr(R2)/(-1)$ ; $R3larr(R3)/4$

$A=((1,0,0,|,9),(0,1,0,|,17/4),(0,0,1,|,-17/4))$

Thus $x=9$ , $y=17/4$ and $z=-17/4$

How do you solve using gaussian elimination or gauss-jordan elimination, x+2y+2z=9x+2y+2z=9x+2y+2z=9, x+y+z=9x+y+z=9x+y+z=9, 3x-y+3z=103x−y+3z=103x-y+3z=10?