How do you solve using gaussian elimination or gauss-jordan elimination, #x_3 + x_4 = 0#, #x_1 + x_2 + x_3 + x_4 = 1#, #2x_1 - x_2 + x_3 + 2x_4 = 0#, #2x_1 - x_2 + x_3 + x_4 = 0#?

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Answer 1 · 2017-12-10T15:22:10

#x_1=1/3#, #x_2=2/3#, #x_3=x_4=0#

From first equation, #x_4=-x_3#

After using this equality into other ones,

#x_1+x_2=1# #(a)#, #2x_1-x_2-x_3=0# #(b)# and #2x_1-x_2=0# #(c)#

From #(c)#, #x_2=2x_1#

After using this equality into other ones,

#x_1+2x_1=1# or #3x_1=1# #(d)# and #2x_1-2x_1-x_3=0# or #-x_3=0# #(e)#

From #(d)#, #x_1=1/3# and #(e)#, #x_3=0#

Hence, #x_2=2/3# from #(c)# and #x_4=0# from first equation.