JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}\). Then the sum of all elements of the matrix \(\text{adj}(\text{adj}(2(\text{adj}A)^{-1}))\) is equal to:
- A \(3\)
- B \(4\)
- C \(-4\)
- D \(-3\)
Answer & Solution
Correct Answer
(D) \(-3\)
Step-by-step Solution
Detailed explanation
The determinant of matrix \(A\) is given by: \(|A| = 1(0 - 3) - 1(-10 - 1) + 2(-6 - 0)\) \(|A| = -3 + 11 - 12 = -4\) We know the property \(A(\text{adj}A) = |A|I\), which gives \(\text{adj}A = |A|A^{-1}\). Taking the inverse on both sides:…
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