JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left(\begin{array}{cc}4 & -2 \\ \alpha & \beta\end{array}\right)\) . If \(A ^{2}+\gamma A +18 I = O\), then \(\operatorname{det}( A )\) is equal to
- A \(-18\)
- B \(18\)
- C \(-50\)
- D \(50\)
Answer & Solution
Correct Answer
(B) \(18\)
Step-by-step Solution
Detailed explanation
The characteristic equation for \(A\) is \(| A -\lambda I |=0\) \(\left|\begin{array}{cc}4-\lambda & -2 \\ \alpha & \beta-\lambda\end{array}\right|=0\) \((4-\lambda)(\beta-\lambda)+2 \alpha=0\) \(\lambda^{2}-(\beta+4) \lambda+4 \beta+2 \alpha=0\) Put \(\lambda= A\)…
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