First slide

Applications of determinant

Question

If $A = [\begin{array}{lll} 1 0 2 \\ 5 1 x \\ 1 1 1 \end{array}]$ is a singular matrix, then x is equal to

Easy

A

3
B

5
C

9
D

11

Solution

As A is a singular matrix,
$| A | = 0 \Rightarrow |\begin{array}{ccc} 1 & 0 & 0 \\ 5 & 1 & x - 10 \\ 1 & 1 & - 1 \end{array}| = 0$
[using $C_{3} \to C_{3} - 2 C_{1}$ ]
$\begin{array}{l} \Rightarrow |\begin{array}{cc} 1 & x - 10 \\ 1 & - 1 \end{array}| = 0 \Rightarrow - 1 ∣ - x + 10 = 0 \\ \Rightarrow x = 9 \end{array}$

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