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CSIR NET Mathematics 2024|Linear Algebra | 20 February 2024

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Question 1

Let a1, a2, anIR be such that a1 + a2 +…+ an = 0 &  then all eigenvalues of A are

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?

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
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Feb 20CSIR NET & SET