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Show that the following system is incons...

Show that the following system is inconsistent.
(a-b)x+(b-c)y+(c-a)z=0
(b-c)x+(c-a)y+(a-b)z=0
(c-a)x+(a-b)y+(b-c)z=1

Text Solution

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`Delta=[[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]] [R_1rarrR_1+R_2+R_3]`
=`[[0,b-c,c-a],[0,c-a,a-b],[0,a-b,b-c]]`=0
`Deltax=[[0,b-c,c-a],[0,c-a,a-b],[1,a-b,b-c]]`
=`(a-b)(b-c)-(c-a)^2ne0`
`therefore` the system is inconsistent.
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