AP EAMCET · Maths · Determinants
If \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]\) and \(\alpha A^2+\beta A=2 I\) for some \(\alpha, \beta, \in R\) then \(\alpha+\beta=\)
- A 7
- B 10
- C 12
- D 5
Answer & Solution
Correct Answer
(B) 10
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given, } A=\left[\begin{array}{cc} 1 & 2 \\ -2 & -5 \end{array}\right] \text {, So, } A^2-(-5+1) A+(-5+4) I=0 \\ \Rightarrow & A^2+4 A=I \Rightarrow 2 A^2+8 A=2 I \end{aligned}\) If we compare with \(\alpha A^2+\beta A=2 I\), we get…
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