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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Determinants

NDA 2021 · Mathematics · Determinants

The element in the i^ th row and the j^ th column of a determinant...

The element in the ith i^{\text{th }} row and the jth j^{\text{th }} column of a determinant of third order is equal to 2(i+j)2(i+j). What is the value of the determinant?

Options

  1. A00
  2. B22
  3. C44
  4. D66

Correct answer

A. 00

Step-by-step solution

Determinant =\left|468681081012\begin{array}{ccc}4 & 6 & 8 \\ 6 & 8 & 10 \\ 8 & 10 & 12\end{array}\right|=2\left|234345456\begin{array}{lll}2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6\end{array}\right|=2[2(24-25)+3(20-18)+4(15-16)]=0.
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