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CSIR NET Mathematics 2022| Linear Algebra (4 OCTOBER)

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Question 1

Let A & B be two n × n matrices over a field F then

Question 2Multiple Correct Options

Let M be a real matrix which has 0, 1, and -1 as eigen values which of the following is  true of M?

Question 3

If  then which of the following is/are true.

Question 4

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 5

Let V be the set of all polynomials of degree 2. Define T: V V by T(p(x)) = p (1) + p (2) x + p (0) x2, p(x) V. Then the trace of the matrix representing T is
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Oct 4CSIR NET & SET