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

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Answer 1 · 2018-04-06T15:10:38

#x=9#, #y=17/4# and #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#