How do you solve the system #3a-3b+4c=-23#, #a+2b-3c=25#, and #4a-b+c=25#?

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Answer 1 · 2017-08-06T08:18:13

The solution is #S = O/#

We perform the Gauss Jordan elimination with the augmented matrix

#((1,2,-3,:,25),(3,-3,4,:,-23),(4,-1,1,:,25))#

#R3larrR3-4R1#, #=>#, #((1,2,-3,:,25),(3,-3,4,:,-23),(0,-9,13,:,-75))#

#R2larrR2-3R1#, #=>#, #((1,2,-3,:,25),(0,-9,13,:,-98),(0,-9,13,:,-75))#

#R3larrR3-R2#, #=>#, #((1,2,-3,:,25),(0,-9,13,:,-98),(0,0,0,:,23))#

#R2larr(R2)/(-9)#, #=>#, #((1,2,-3,:,25),(0,1,-13/9,:,98/9),(0,0,0,:,23))#

#R1larrR1-2R2#, #=>#, #((1,0,-1/9,:,29/9),(0,1,-13/9,:,98/9),(0,0,0,:,23))#

The system of equations is inconsistent.