First slide

Introduction to Determinants

Question

Let $D_{1} = |\begin{array}{lll} a b a + b \\ c d c + d \\ a b a - b \end{array}|$ and $D_{2} = |\begin{array}{ccc} a & c & a + c \\ b & d & b + d \\ a & c & a + b + c \end{array}|$ then the value of $|\frac{D_{1}}{D_{2}}|, where b \neq 0 and ad \neq bc$ , is

Moderate

Solution

Using $C_{3} \to C_{3} - (C_{1} + C_{2})$ in D₁, and D₂,wa have
$\frac{D_{1}}{D_{2}} - \frac{- 2 b (ad - bc)}{b (ad - bc)} = - 2$

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