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Engineering Maths · Q24

Linear Algebra

Engineering and GATE · Engineering Maths · question 24

Q24

Which one of the following statements is TRUE about every n × n matrix with only real eigen values?

A.
If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigen values is negative
Answer
B.
If the trace of the matrix is positive, all its eigen values are positive
C.
If the determinant of the matrix is positive, all its eigen values are positive
D.
If the product of the trace and determinant of the matrix is positive, all its eigen values are positive

Answer: Option A

Solution

Answer: Option A
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