JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A = \begin{bmatrix} 1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1 \end{bmatrix}\) be a singular matrix. Let \(f(x) = \int\limits_0^x (t^2 + 2t + 3)\,dt\), \(x \in [1, \alpha]\). If \(M\) and \(m\) are respectively the maximum and the minimum values of \(f\) in \([1, \alpha]\), then \(3(M - m)\) is equal to :
- A \(64\)
- B \(68\)
- C \(72\)
- D \(76\)
Answer & Solution
Correct Answer
(B) \(68\)
Step-by-step Solution
Detailed explanation
Since \(A\) is a singular matrix, \(|A| = 0\). \(|A| = 1(-1 - \alpha) - 3(-2 - 0) - 1(2 - 0) = 0\) \(-1 - \alpha + 6 - 2 = 0 \Rightarrow \alpha = 3\) The function is \(f(x) = \int\limits_0^x (t^2 + 2t + 3)\,dt = \dfrac{x^3}{3} + x^2 + 3x\) Differentiating with respect to \(x\),…
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