Consider the matrix
\(A = \left[ {\begin{array}{*{20}{c}} {{a^2}}&{ab}&{ac}\\ {ab}&{{b^2}}&{bc}\\ {ac}&{bc}&{{c^2}} \end{array}} \right]\)
Where a, b, and c are a non-zero real number. Then the matrix has1
three non-zero real eigenvalues
2
complex eigenvalues
3
Two non-zero eigenvalue
4
Only one non-zero eigenvalue