MCQ
Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in R$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to -
- A$-10$
- B$-6$
- C$6$
- ✓$10$
$|A-\lambda I|=0$$\left|\begin{array}{cc}1-\lambda & 2 \\2 & -5-\lambda\end{array}\right|=0$
$\lambda^{2}+4 \lambda=1$
$A^{2}+4 A=I$
$2\,A^{2}+8 A=2 I$
Given that $\alpha A^{2}+\beta A=2\,I$
Comparing equation $(1)$ and $(2)$ we get
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