WBJEE · Maths · Matrices
Let \(\mathrm{A}=\left(\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ c & \mathrm{~d}\end{array}\right)\) be a \(2 \times 2\) real matrix with \(\operatorname{det} \mathrm{A}=1\). If the equation \(\operatorname{det}\left(\mathrm{A}-\lambda \mathrm{I}{2}\right)=0\) has imaginary roots \(\left(\mathrm{I}{2}\right.\) be the
Identity matrix of order 2), then
- A \((a+d)^{2} < 4\)
- B \((a+d)^{2}=4\)
- C \((a+d)^{2}>4\)
- D \((a+d)^{2}=16\)
Answer & Solution
Correct Answer
(A) \((a+d)^{2} < 4\)
Step-by-step Solution
Detailed explanation
Hint: \(|\mathrm{A}|=0 \therefore \mathrm{ad}-\mathrm{bc}=1\) \(\left|\mathrm{~A}-\lambda \mathrm{I}_{2}\right|=0\) \(\left|\begin{array}{cc}\mathrm{a}-\lambda & \mathrm{b} \\ \mathrm{c} & \mathrm{d}-\lambda\end{array}\right|=0\)…
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