JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(M=\left\{A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{\pm 3, \pm 2, \pm 1,0\}\right\} .\) Define \(f: M \rightarrow z\), as \(f(A)=\operatorname{det}(A)\) for all \(A \in M\), where \(Z\) is set of all integers. Then the number of \(A \in M\) such that \(f(A)=15\) is equal to \(.....\)
- A \(16\)
- B \(32\)
- C \(48\)
- D \(71\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\(|\mathrm{A}|=\mathrm{ad}-\mathrm{bc}=15\) where \(a, b, c, d \in\{\pm 3, \pm 2, \pm 1,0\}\) Case \(\mathrm{I} \mathrm{ad}=9 \,\& \,\mathrm{bc}=-6\) For ad possible pairs are \((3,3),(-3,-3)\) For bc possible pairs are \((3,-2),(-3,2),(-2,3),\left(2_{6}-3\right)\) So total…
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