The value of the determinant b2-ab b-c bc-ac ab-a2 a-b b2-ab bc-ac c-a ab-a2 -

The correct option is C 0 b^2 ab #160; b c bc ac amp; #160; amp; ab a^2 a b b^2 ab amp; #160; amp; #160; bc ac ...

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Determinant

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The value of the determinant $∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b b - c b c - a c a b - a^{2} a - b b^{2} - a b b c - a c c - a a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ =

a b c

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a + b + c

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0

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a b + b c + c a

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∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

|\begin{matrix} b^{2} - a b & b - c & b c - a c \\ a b - a^{2} & a - b & b^{2} - a b \\ b c - c a & c - a & a b - a^{2} \end{matrix}|

a b c (b - c) (c - a) (a - b)

(b - c) (c - a) (a - b)

(a + b + c) (b - c) (c - a) (a - b)

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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