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

1 Answer
Jan 6, 2018

Answer:

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

Explanation:

#([-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)]"#