Linear Algebra GATE 2014 Question #9965 with Solution

GATE 2014 · session-3

Engineering MathematicsLinear AlgebraeasyMCQ1 mark

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

AIf the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.BIf the trace of the matrix is positive, all its eigenvalues are positive.CIf the determinant of the matrix is positive, all its eigenvalues are positive.DIf the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.

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