How to solve the system of equation using matrices? Thanks!

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Feb 22, 2018

Answer:

#x=1#, #y=-4# and #z=-2#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

#A=((1,1,1,|,-5),(1,-1,3,|,-1),(4,1,1,|,-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

#R2larrR1-R2#; #R3larrR3-4R1#

#A=((1,1,1,|,-5),(0,-2,2,|,4),(0,-3,-3,|,18))#

#R2larr(R2)/(-2)#

#A=((1,1,1,|,-5),(0,1,-1,|,-2),(0,-3,-3,|,18))#

#R3larrR3+3R2#

#A=((1,1,1,|,-5),(0,1,-1,|,-2),(0,0,-6,|,12))#

#R3larr(R2)/(-6)#

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

#R1larrR1-R3; R2larrR2+R3#

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

#R1larrR1-R2#

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

Thus, #x=1#, #y=-4# and #z=-2#

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