Class CBSE Class 12 Mathematics Matrices and Determinants Q #731
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
\(If~A=\begin{bmatrix}-2&0&0\\ 1&2&3\\ 5&1&-1\end{bmatrix},\) then the value of | A (adj. A) | is:
(A) 100 I
(B) 10 I
(C) 10
(D) 1000
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AI Tutor Explanation

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Step-by-Step Solution

  1. First, find the determinant of matrix A:

    |A| = -2 * (2*(-1) - 3*1) - 0 + 0 = -2 * (-2 - 3) = -2 * (-5) = 10

  2. We know that |A (adj. A)| = |A|n, where n is the order of the matrix A.

    Here, A is a 3x3 matrix, so n = 3.

  3. Therefore, |A (adj. A)| = |A|3 = (10)3 = 1000

Correct Answer: 1000

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply the properties of determinants and adjoints of matrices to find the value of the given expression.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, namely, applying the property |A(adj A)| = |A|^n, where n is the order of the matrix, and then calculating the determinant of A.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of a specific property related to matrices and determinants, which is typically covered in textbooks.

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