How do you solve using gaussian elimination or gauss-jordan elimination, $-2x -5y +5z =4$ , $-3x -y -z =10$ , $5x +3y -z =10$ ?

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Answer 1 · 2018-01-06T20:17:24

$P="[(43,-46,-28)]"$

$([-2,-5,5,|,4],[-3,-1,-1,|,10],[5,3,-1,|,10])$
$R_1=R_1xx5$
$R_2=R_2xx5$
$R_3=R_3xx3$

$([-10,-25,25,|,20],[-15,-5,-5,|,50],[15,9,-3,|,30])$
$R_2=R_2+R_3$
$R_3=R_3xx2/3$

$([-10,-25,25,|,20],[0,4,-8,|,80],[10,6,-2,|,20])$
$R_3=R_3+R_1$
$R_1=R_1xx1/5$
$R_2=R_2xx1/4$

$([-2,-5,5,|,4],[0,1,-2,|,20],[0,-19,23,|,40])$
$R_3=R_3+19xxR_2$

$([-2,-5,5,|,4],[0,1,-2,|,20],[0,0,-15,|,40+20xx19])$
$R_3=R_3xx-1/15$

$([-2,-5,5,|,4],[0,1,-2,|,20],[0,0,1,|,-(cancel5xx8+cancel5xx4xx19)/(cancel5xx3)])$
$R_2=R_2+2xxR_3$

$([-2,-5,5,|,4],[0,1,0,|,20-2xx(4xx(2+19))/(3)],[0,0,1,|,-(4xx(2+19))/(3)])$
Simplifing right side

$([-2,-5,5,|,4],[0,1,0,|,(60-2xx84)/3],[0,0,1,|,-84/3])$
$R_1=R_1+5xxR_2$
$R_1=R_1-5xxR_3$
$R_1=R_1xx-1/2$

$([1,0,0,|,-2+5xx(60-198)/-6-5xx(-84/-6)],[0,1,0,|,(60-198)/3],[0,0,1,|,-28])$
Simplifing right side

$([1,0,0,|,-2+5xx6xx(10-33)/-6-5xx6xx(14/6)],[0,1,0,|,(60-198)/3],[0,0,1,|,-28])$

$color(red)x=-2-5xx(10-33)-5xx14=-2+115-70color(red)(=43)$

$color(red)y=(60-198)/3=20-66color(red)(=-46)$

$color(red)(z=-28)$

$P="[(43,-46,-28)]"$

How do you solve using gaussian elimination or gauss-jordan elimination, -2x -5y +5z =4-2x -5y +5z =4, -3x -y -z =10-3x -y -z =10, 5x +3y -z =105x +3y -z =10?