Class CBSE Class 12 Mathematics Matrices and Determinants Q #735
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
If \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then \(A^{-1}\) is:
(A) \([\begin{matrix}\frac{1}{2}&0&0\\ 0&3&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(B) \(30[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(C) \(\frac{1}{30}[\begin{matrix}2&0&0\\ 0&3&0\\ 0&0&5\end{matrix}]\)
(D) \(\frac{1}{30}[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
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Step-by-Step Solution

  1. Given the matrix \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix}\).

  2. Since A is a diagonal matrix, its inverse \(A^{-1}\) is also a diagonal matrix with the reciprocals of the diagonal elements of A.

  3. Therefore, \(A^{-1} = \begin{bmatrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{bmatrix}\).

Correct Answer: \(\begin{bmatrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{bmatrix}\)

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply the formula and steps to calculate the inverse of a matrix.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (calculating the inverse of a matrix) rather than recalling facts or understanding concepts.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of matrix inverses as covered in the textbook.

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