Topic: Engineering Mathematics
Eigen values of $\begin{bmatrix}-5 & 2 \\ 2 & -2\end{bmatrix}$ are
- A. -6, -1
- B. 6, -1
- C. -6, 1
- D. 6, 1
Answer: A. -6, -1
Explanation: For eigenvalues, $|A-\lambda I|=0$. $\begin{vmatrix}-5-\lambda & 2 \\ 2 & -2-\lambda\end{vmatrix}=0 \implies (-5-\lambda)(-2-\lambda) - 4 = 0 \implies 10 + 5\lambda + 2\lambda + \lambda^{2} - 4 = 0 \implies \lambda^{2} + 7\lambda + 6 = 0$. Factoring gives $(\lambda+6)(\lambda+1)=0$, so $\lambda=-6$ and $\lambda=-1$.