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Que. Which one of the following statements is TRUE about every n×n matrix with only real eigenvalues?
a. If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.
b. If the trace of the matrix is positive, all its eigenvalues are positive.
c. If the determinant of the matrix is positive, all its eigenvalues are positive.
d. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
Answer:If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.
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