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: The characteristic equation is given by $\det(A-\lambda I)=0$. This becomes $(-5-\lambda)(-2-\lambda)-4=0$, which simplifies to $\lambda^{2}+7\lambda+6=0$. Factoring this gives $(\lambda+6)(\lambda+1)=0$, leading to the eigenvalues $\lambda = -1, -6$.