Solving a linear system? x+2y+z=2 3x+8y+z=12 4y+z=2

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Answer 1 · 2018-07-04T10:49:08

#x=2#, #y=1# and #z=-2#

Perform the Gauss Jordan elimination on the augmented matrix

#A=((1,2,1,|,2),(3,8,1,|,12),(0,4,1,|,2))#

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

#R2larrR2-3R1#

#A=((1,2,1,|,2),(0,2,-2,|,6),(0,4,1,|,2))#

#R3larrR3-2R2#

#A=((1,2,1,|,2),(0,2,-2,|,6),(0,0,5,|,-10))#

#R3larr(R3)/5#

#A=((1,2,1,|,2),(0,2,-2,|,6),(0,0,1,|,-2))#

#R1larrR1-R3#; #R2larrR2+2R3#

#A=((1,2,0,|,4),(0,2,0,|,2),(0,0,1,|,-2))#

#R1larrR1-R2#;

#A=((1,0,0,|,2),(0,1,0,|,1),(0,0,1,|,-2))#

#R2larr(R2)/2#

Thus #x=2#, #y=1# and #z=-2#