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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

If A=[ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] , then what...

If A=\left[100010001\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right], then what is 23A3−19A2−4A23 A^3-19 A^2-4 A equal to?

Options

  1. ANull matrix of order 3
  2. BIdentity matrix of order 3
  3. C\left[200020002\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]
  4. D\left[700070007\begin{array}{lll}7 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7\end{array}\right]

Correct answer

A. Null matrix of order 3

Step-by-step solution

Since, A=\left[100010001\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]=I\mathrm{A}^{\mathrm{n}}=\mathrm{I} (identity matrix) Now, 23A3−19A2−4A2323 \mathrm{ A}^3-19 \mathrm{ A}^2-4 \mathrm{ A}23\mathrm{I}−19-19\mathrm{I}−4-4\mathrm{I}=O=\mathrm{O}
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