Let Δ$$=det$$⁡a b cb c ac a b . Then which of the following statements is false for a,b,c∈R ?

Correct option is 3Δ=0 if and only if a=b=c

Questions

$Let Δ = \det (\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}) . Then which of the following statements is false for a, b, c \in R ?$

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Δ>0 if a=−1, b=−2, c=−3

Δ<0 if a=1, b=2, c=3

Δ=0 if and only if a=b=c

Δ=0 if and only if a3+b3+c3=3abc

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detailed solution

Correct option is C

Δ=−a3+b3+c3−3abc=−12(a+b+c)(a−b)2+(b−c)2+(c−a)2

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Let Δ=det⁡a b cb c ac a b . Then which of the following statements is false for a,b,c∈R ?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$Let Δ = \det (\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}) . Then which of the following statements is false for a, b, c \in R ?$