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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
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
    $6$
  • ✓
    $10$
✓

Answer

Correct option: D.
$10$
d
Sol. Characteristic equation of matric $A$

$|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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