begin vmatrix a-b - a-2 b - a-3 ba-2 b - a-3 b - a-4 ba-4 b - a-5 b - a-6 bend vmatrix -1

The correct option is C 0a+b amp; a+2b amp; a+3b a+2b amp; a+3b amp; a+4b a+4b amp; a+5b amp; a+6b = a+b amp; a+2b amp; a+3b b am ...

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Properties of Determinants

begin vmatrix...

Question

$∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣ =$

a^{2} + b^{2} + c^{2} - 3 a b c

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3ab

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3a+5b

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Solution

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∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 a \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 c \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + 2 b a + 2 b & a & a + b a + b & a + 2 b & a \end{matrix} ∣ ∣ ∣ ∣ = 9 b^{2} (a + b)

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