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# gauss elimination with parameters

Posted on 2008-11-19

I'm breaking my head trying to figure out what i'm doing wrong,

i'm support to eliminate the following equations using Gauss elimination system

ax+y+z=4

x+by+z=3

x+2by+z=4

and i'm suppose to figure out for which a,b (which are Parameters) the system has One solution/Infinit Solutions/No solutions - if there's infint solutions i'm suppose to write the general solution for the system.

now it's all pretty basic in the begining

1 b 1 3

1 2b 1 4 R2->R2-R1

a 1 1 4 R3->R3-aR1

which leads me to

1 b 1 3

0 b 0 1 * i can reach the first value using /:b , i then get y=1/b

0 1-ab 1-a 4-3a

from here i'm puzzled as there's no way to carry on the elimination (if i'm doing it right)