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If , then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :

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NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper
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  1. −16 
  2. 14 
  3. −14
  4. 16

Answer (Detailed Solution Below)

Option 2 : 14 
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Detailed Solution

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Concept:

The trace of a matrix expression is the sum of the diagonal elements of the resulting matrix. The trace of a sum of matrices is the sum of their traces. Also, the trace of any power of a matrix can be computed using the cyclic properties of matrix multiplication if eigenvalues are known or the matrix is triangularizable.

Calculation:

Given:

We are to find:

Since A is upper triangular, powers of A remain upper triangular, and the trace of An is simply the sum of powers of diagonal elements.

Diagonal elements of A: 1 and -1

So, for each power:

Now compute each term:

Now compute total:

 

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Last updated on Jun 12, 2025

-> NIELIT Scientific Assistant city intimation slip 2025 has been released at the official website.

-> NIELIT Scientific Assistant exam 2025 is scheduled to be conducted on June 28. 

-> A total number of 113 revised vacancies have been announced for the post of Scientific Assistant in Computer Science (CS), Information Technology (IT), and Electronics & Communication (EC) streams.

-> Online application form, last date has been extended up to from 17th April 2025.

->The NIELT has revised the Essential Qualifications for the post of Scientific Assistant. Candidates must possess (M.Sc.)/ (MS)/ (MCA) / (B.E.)/ (B.Tech) in relevant disciplines.

 

-> The NIELIT Scientific Assistant 2025 Notification has been released by the National Institute of Electronics and Information Technology (NIELIT).

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