How do you solve using gaussian elimination or gauss-jordan elimination, #x_1+x_2+x_3=3#, #x_1+2x_2-x_3=2#, #2x_1+x_2+2x_3=5#?

1 Answer
Alan P.
Nov 7, 2016

#(x_1,x_2,x_3)=(1,1,1)#

Explanation:

Initial Augmented Matrix:
#color(white)("XXXXXX")x_1color(white)("XXXXXX")x_2color(white)("XXXXX")x_3#
#( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXX")-1,color(white)("XXXXX")2), (color(white)("XXXXX")2,color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXXX")5) )#

Pivot Row: 1 Pivot Column: 1
pivot Row reduced:
#( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXX")-1,color(white)("XXXXX")2), (color(white)("XXXXX")2,color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXXX")5) )#

Non-pivot rows reduced for pivot column
#( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXX")-1,color(white)("XXXXX")0,color(white)("XXXX")-1) )#

Pivot Row: 2 Pivot Column: 2
pivot Row reduced:
#( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXX")-1,color(white)("XXXXX")0,color(white)("XXXX")-1) )#

Non-pivot rows reduced for pivot column
#( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")3,color(white)("XXXXX")4), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXX")-2,color(white)("XXXX")-2) )#

Pivot Row: 3 Pivot Column: 3
pivot Row reduced:
#( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")3,color(white)("XXXXX")4), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")1) )#

Non-pivot rows reduced for pivot column
#( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")1) )#

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