Class CBSE Class 12 Mathematics Matrices and Determinants Q #756
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If \(A=[a_{ij}]\) is a \(3\times3\) diagonal matrix such that \(a_{11}=1\), \(a_{22}=5\) and \(a_{33}=-2\), then \(|A|\) is:
(A) 0
(B) -10
(C) 10
(D) 1
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AI Tutor Explanation

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Step-by-Step Solution

  1. A diagonal matrix \(A\) is given as:

    \(A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}\)

  2. The determinant of a diagonal matrix is the product of its diagonal elements.

  3. Therefore, \(|A| = 1 \times 5 \times (-2)\)

  4. \(|A| = -10\)

Correct Answer: -10

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of diagonal matrices and determinants to calculate the value.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a procedure to calculate the determinant of a diagonal matrix. This involves multiplying the diagonal elements.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of the properties of diagonal matrices and how to calculate their determinants, which is a standard textbook concept.

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