First slide

Introduction to Determinants

Question

Let $Δ (x, y) = |\begin{array}{ccc} 1 & x & y \\ 1 & x + y & y \\ 1 & x & x + y \end{array}|$ .Then $Δ (- 3, 2)$ equal to

Moderate

A

13
B

-6
C

12
D

-5

Solution

Using $R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}$ we get
$Δ (x, y) = |\begin{array}{lll} 1 x y \\ 0 y 0 \\ 0 0 x \end{array}| = x y$
$∴ Δ (- 3, 2) = - 6$

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