The value of determinant is a-b a-2b a-3b a-2b a-3b a-4b a-4b a-5b a-6b is -

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Properties of Determinants

The value of ...

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The value of determinant is $∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣$ is ________.

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

∣ ∣ ∣ ∣ \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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