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CSIR NET Mathematics 2024|Linear Algebra | 20 February 2024
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Question 1
Let a1, a2, an∈IR be such that a1 + a2 +…+ an = 0 &
then all eigenvalues of A are
![](https://gradeup-question-images.grdp.co/liveData/PROJ106037/1655107958073613.png)
Question 2
Let A be the n × n matrix whose main diagonal entries are zero and elsewhere 1
i.e., aii = 0, 1 ≤ i ≤ n & aij = 1, i ≠ j then what are eigenvalues of A
Question 3Multiple Correct Options
If
then which of the following are true?
![](https://gradeup-question-images.grdp.co/liveData/PROJ106037/1655107967680859.png)
Question 4
Let A be an n × n matrix such that the set of all non-zero eigen values has exactly r elements which of the following is true
Question 5Multiple Correct Options
Let
∈ Mn (
) and |A| = 1 If |a+d| > 2 then for which value of λ, A is not similar to
![](https://gradeup-question-images.grdp.co/liveData/PROJ106037/1655107973766257.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ106037/1655107974443818.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ106037/1655107975138254.png)
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Feb 20CSIR NET & SET