Q.
Consider the system of equations ax+by+cz=2,bx+cy+az=2,cx+ay+bz=2where a,b,c are real numbers such that a+b+c=0then the system
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a
Has two solutions
b
Inconsistent
c
Has unique solution
d
has infinitely many solution
answer is B.
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Detailed Solution
Augmented matrix AD=abc2bca2cab2 R3→R1+R2+R2 ~abc2bca2a+b+ca+b+ca+b+c6 ~abc2bca20006 ∵a+b+c=0Here rankA=2 and rankAD=3∴rankA≠rankAD The given system is inconsistent
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