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

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Answer 1 · 2018-01-09T17:03:50

#x=2#, #y=0# and #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#