JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
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 \(6\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
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…
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