Topic: Engineering Mathematics
Find the Eigen values in the system $\begin{bmatrix}4 & 1 \\ 3 & 2\end{bmatrix} \begin{bmatrix}x \\ y\end{bmatrix} = \lambda \begin{bmatrix}x \\ y\end{bmatrix}$
- A. 1 and 5
- B. 4 and 3
- C. 1 and 2
- D. 2 and 4
Answer: A. 1 and 5
Explanation: The characteristic equation is $|A - \lambda I| = 0$. This gives $(4-\lambda)(2-\lambda) - 3 = 0$. Expanding this, we get $\lambda² - 6\lambda + 8 - 3 = 0$, which simplifies to $\lambda² - 6\lambda + 5 = 0$. Factoring gives $(\lambda-5)(\lambda-1)=0$, so the eigenvalues are $\lambda = 1, 5$.