First slide

Introduction to Determinants

Question

The value of $|\begin{matrix} (a + 1) (a + 2) & a + 2 & 1 \\ (a + 2) (a + 3) & a + 3 & 1 \\ (a + 3) (a + 4) & a + 4 & 1 \end{matrix}|$ is

Moderate

A

$(a + 2) (a + 3) (a + 4)$
B

$(a + 1) (a + 2) (a + 3)$
C

0
D

-2

Solution

The given determinant is

$|\begin{matrix} (a + 1) (a + 2) & a + 2 & 1 \\ (a + 2) (a + 3) & a + 3 & 1 \\ (a + 3) (a + 4) & a + 4 & 1 \end{matrix}|$

apply the row operations $R_{2} \to R_{2} \to R_{1}, R_{3} \to R_{3} - R_{2}$
$|\begin{matrix} (a + 1) (a + 2) & a + 2 & 1 \\ 2 (a + 2) & 1 & 0 \\ 2 (a + 3) & 1 & 0 \end{matrix}|$ = $- 2$

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