Question

The matrix \(\left[ {\begin{array}{*{20}{c}} 1&2&4\\ 3&0&6\\ 1&1&P \end{array}} \right]\)has one eigenvalue equal to 3. The sum of the other two eigenvalues is
1. P
2. P – 1
3. P – 2
4. P - 3

Answer 1

Correct Answer - Option 3 : P – 2

Sum of the eigen values of matrix is = Sum of diagonal values present in the matrix

∴ 1 + 0 + P = 3 + λ₂ + λ₃

⇒ P + 1 = 3 + λ₂ + λ₃

⇒ λ₂ + λ₃ = P + 1 – 3 = P – 2