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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

If A=[ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] , then which...

If A=\left[200030004\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right], then which of the following statements are correct? 1. AnA^n will always be singular for any positive integer nn. 2. An\mathrm{A}^{\mathrm{n}} will always be a diagonal matrix for any positive integer n. 3. An\mathrm{A}^{\mathrm{n}} will always be a symmetric matrix for any positive integer n. Select the correct answer using the code given below:

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1, 2 and 3

Correct answer

B. 2 and 3 only

Step-by-step solution

Given A=A=\left[200030004\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]isanon−zerodiagonalmatrixSois a non-zero diagonal matrix SoA^nisalsonon−zerodiagonalmatrixforanyis also non-zero diagonal matrix for anyn \in \mathbb{N} and diagonal elements of AA are positive so AnA^n is also symmetric thus the statements 2 and 3 are correct.
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