lf is a singular matrix, then x is equal to

Engineering

Mathematics

Introduction to Determinants

Properties of Determinant

Question

lf $∣ \begin{array}{lll} 1 & 2 & x \\ 4 & - 1 & 7 \\ 2 & 4 & - 6 \end{array} ∣$ is a singular matrix, then x is equal to

– 3

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Given $A = ∣ \begin{array}{lll} 1 & 2 & x \\ 4 & - 1 & 7 \\ 2 & 4 & - 6 \end{array} ∣$ is a singular matrix

So, detA = 0

⇒ 1(6 – 28) – 2(– 24 – 14) + x(16 + 2) = 0
⇒ – 22 + 76 + 18x = 0

⇒ 18x = – 54

∴ x = – 3