First slide

Introduction to Determinants

Question

$If p, q, r are negative and distinct, then the determinant Δ = |\begin{array}{l} p & q & r \\ q & r & p \\ r & p & q \end{array}| is$

Moderate

A

$\leq - 2$
B

$\leq 0$
C

0
D

>0

Solution

$Δ = \underset{- v e}{\underset{}{- (p + q + r)}} \underset{+ v e}{\underset{}{(p^{2} + q^{2} + r^{2} - p q - q r - r p)}}$
$\Rightarrow Δ > 0$

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