JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(2 \times 2\) real matrix and \(I\) be the identity matrix of order \(2\) . If the roots of the equation \(|A-x I|=0\) be \(-1\) and \(3\) , then the sum of the diagonal elements of the matrix \(A^2\) is ...........
- A \(5\)
- B \(4\)
- C \(10\)
- D \(9\)
Answer & Solution
Correct Answer
(C) \(10\)
Step-by-step Solution
Detailed explanation
\(|A-x I|=0\) Roots are \(-1\) and \(3\) Sum of roots \(=\operatorname{tr}(A)=2\) Product of roots \(=|\mathrm{A}|=-3\) Let \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) We have \(\mathrm{a}+\mathrm{d}=2\) \(\mathrm{ad}-\mathrm{bc}=-3\)…
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