First slide

Introduction to Determinants

Question

$Δ = |\begin{array}{ccc} a & a^{2} & 0 \\ 1 & 2 a + b & (a + b) \\ 0 & 1 & 2 a + 3 b \end{array}|$ is divisible by

Moderate

A

a + b
B

a + 2b
C

2a + 3b
D

a²

Solution

$\begin{matrix} Δ = |\begin{array}{ccc} a & a^{2} & 0 \\ 1 & 2 a + b & (a + b) \\ 0 & 1 & 2 a + 2 b \end{array}| \\ = a |\begin{array}{ccc} 1 & a & 0 \\ 1 & (2 a + b) & (a + b) \\ 0 & 1 & 2 a + 3 b \end{array}| \\ = a (a + b) |\begin{array}{ccc} 1 & a & 0 \\ 0 & 1 & (a + b) \\ 0 & 1 & 2 a + 3 b \end{array}| (R_{2} \to R_{2} - R_{1}) \\ = a (a + b) (2 a + 3 b - a - b) \\ = a (a + b) (a + 2 b) \end{matrix}$

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