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Evaluation of a Determinant

Evaluate x ...

Question

Evaluate $∣ ∣ ∣ \begin{matrix} x & x + 1 x - 1 & x \end{matrix} ∣ ∣ ∣$

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Solution

Given: $∣ ∣ ∣ \begin{matrix} x & x + 1 x - 1 & x \end{matrix} ∣ ∣ ∣$
$= (x) (x) - (x - 1) (x + 1)$
$= x^{2} - (x^{2} - 1)$
$= x^{2} - x^{2} + 1$
$= 1$

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Evaluation of a Determinant

Standard XII Mathematics

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