First slide

Introduction to Determinants

Question

Let $Δ = |\begin{array}{lll} 1 a a^{2} - b c \\ 1 b b^{2} - c a \\ 1 c c^{2} - a b \end{array}|$ , then $∆$ is equal to

Moderate

A

0
B

$a + b + c$
C

$\frac{1}{2} (a^{2} + b^{2} + c^{2})$
D

none of these

Solution

Applying $R_{2} \to R_{2} - R_{1} + R_{3} \to R_{3} - R_{1}$ we get
$Δ = (b - a) (c - a) |\begin{array}{lll} 1 a a^{2} - b c \\ 0 1 a + b + c \\ 0 1 a + b + c \end{array}| = 0$
$[∵ R_{2} and R_{3} are identical]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App