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$a \neq b \neq c \neq 1, a x + y + z = 0, x + b y + z = 0, x + y + c z = 0$ have non-trivial solutions then $a + b + c - a b c =_______$

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Correct option is C

Since the system has non-trivial solution, we have Δ=0⇒a111b111c=0⇒a(bc-1)-1(c-1)+1(1-b)=0⇒abc-a-c+1+1-b=0⇒a+b+c-abc=2

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a≠b≠c≠1, ax+y+z=0, x+by+z=0, x+y+cz=0 have non-trivial solutions thena+b+c−abc=_______

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$a \neq b \neq c \neq 1, a x + y + z = 0, x + b y + z = 0, x + y + c z = 0$ have non-trivial solutions then $a + b + c - a b c =_______$