A-b b-c c-a b-c c-a a-b c-a a-b b-c is equal to

The correct option is C 0 D= a b amp; b c amp; c a b c amp; c a amp; a b c a amp; a b amp; b c R _ 1 ⟶ R _ 1 + R _ ...

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Definition of a Determinant

a-b b-c c...

Question

$∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a b - c & c - a & a - b c - a & a - b & b - c \end{matrix} ∣ ∣ ∣ ∣$ is equal to

a b c

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2 a b c

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0

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4 a b c

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Solution

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Similar questions

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

∣ ∣ ∣ ∣ \begin{matrix} a + b & b + c & c + a b + c & c + a & a + b c + a & a + b & b + c \end{matrix} ∣ ∣ ∣ ∣ = K ∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣

K =

|\begin{matrix} a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c \end{matrix}| = 2 |\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix}|

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

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

= 0

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