Evaluate 1&x&y 1&x+y&y 1&x&x+y - Vidyadip

Question

Evaluate $\begin{vmatrix}1&\text{x}&\text{y}\\1&\text{x}+\text{y}&\text{y}\\1&\text{x}&\text{x+y}\end{vmatrix}$

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Answer

$\triangle=\begin{vmatrix}1&\text{x}&\text{y}\\1&\text{x}+\text{y}&\text{y}\\1&\text{x}&\text{x+y}\end{vmatrix}$
Applying R₂ → R₂ - R₁ and R₃ → R₃ - R₁, we have:
$\triangle=\begin{vmatrix}1&\text{x}&\text{y}\\0&\text{y}&0\\0&0&\text{x}\end{vmatrix}$
Expanding along C₁, we have:
$\triangle$ = 1(xy - 0) = xy

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