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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Determinants

NDA 2021 · Mathematics · Determinants

With the numbers 2,4,6,8 , all the possible determinants with these...

With the numbers 2,4,6,82,4,6,8, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?

Options

  1. A128128
  2. B6464
  3. C3232
  4. D00

Correct answer

D. 00

Step-by-step solution

All possible determinants from 2,4,62,4,6 and 8 \left|8642\begin{array}{ll}8 & 6 \\ 4 & 2\end{array}\right|+\left|8426\begin{array}{ll}8 & 4 \\ 2 & 6\end{array}\right|+\left|2486\begin{array}{ll}2 & 4 \\ 8 & 6\end{array}\right|+\left|4268\begin{array}{ll}4 & 2 \\ 6 & 8\end{array}\right|+\left|4862\begin{array}{ll}4 & 8 \\ 6 & 2\end{array}\right|+\left|6824\begin{array}{ll}6 & 8 \\ 2 & 4\end{array}\right|=(16−24)+(48−8)+(12−32)+(32−12)+(8−48)+(24−16)=0\begin{aligned} &=(16-24)+(48-8)+(12-32)+(32-12) \\ &+(8-48)+(24-16) \\ &=0\end{aligned}$$
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