is equal to ?

Engineering

Mathematics

Introduction to Determinants

Properties of Determinant

Question

$∣ \begin{array}{ccc} 2^{3} & 3^{3} & 3 . 2^{2} + 3.2 + 1 \\ 3^{3} & 4^{3} & 3 . 3^{2} + 3.3 + 1 \\ 4^{3} & 5^{3} & 3 . 4^{2} + 3.4 + 1 \end{array} ∣$ is equal to ?

None of these

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$∣ \begin{array}{ccc} 2^{3} & 3^{3} & 3 . 2^{2} + 3.2 + 1 \\ 3^{3} & 4^{3} & 3 . 3^{2} + 3.3 + 1 \\ 4^{3} & 5^{3} & 3 . 4^{2} + 3.4 + 1 \end{array} ∣$

$|\begin{array}{lll} 2^{3} 3^{3} 3^{3} - 2^{3} \\ 3^{3} 4^{3} 4^{3} - 3^{3} \\ 4^{3} 5^{3} 5^{3} - 4^{3} \end{array}|$

C₃ → C₃ + C₁

$|\begin{array}{lll} 2^{3} 3^{3} 3^{3} \\ 3^{3} 4^{3} 4^{3} \\ 4^{3} 5^{3} 5^{3} \end{array}| = 0$