symmetric matrix

Let v₁ and v₂ be the two eigenvectors corresponding to distinct eigenvalues of a 3 × 3 real symmetric matrix. Which one of the following statements is true?

The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & 0 & {{3 \over 2}} \cr } } \right]$$ has three distinct eigen values and o...