How do you solve using gaussian elimination or gauss-jordan elimination, #2x + 4y−6z = 42#, #x + 2y+ 3z = 3#, #3x−4y+ 4z = −16#?

1 Answer
Nov 20, 2017

Answer:

The solution is #((x),(y),(z))=((4),(4),(-3))#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

#A=((1,2,-3,|,21),(1,2,3,|,3),(3,-4,4,|,-16))#

Perform the row operations

#R2larrR2-R1# and #R3larrR3-3R1#

#A=((1,2,-3,|,21),(0,0,6,|,-18),(0,-10,13,|,-79))#

#R2harrR3# and #R3larr(R3)/6#

#A=((1,2,-3,|,21),(0,-10,13,|,-79),(0,0,1,|,-3))#

#R2larr(R2-13R3)# and #R2larr(R2)/(-10)#

#A=((1,2,-3,|,21),(0,1,0,|,4),(0,0,1,|,-3))#

#R1larr(R1-2R2)# and #R1larrR1+3R3#

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