Class CBSE Class 12 Mathematics Matrices and Determinants Q #770
KNOWLEDGE BASED
REMEMBER
1 Marks 2025 MCQ SINGLE
The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a/an:
(A) scalar matrix
(B) identity matrix
(C) null matrix
(D) symmetric matrix
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Step-by-Step Solution

  1. Definition of Scalar Matrix: A scalar matrix is a diagonal matrix where all the diagonal elements are equal.
  2. Definition of Identity Matrix: An identity matrix is a diagonal matrix where all the diagonal elements are equal to 1.
  3. Definition of Null Matrix: A null matrix is a matrix where all the elements are zero.
  4. Definition of Symmetric Matrix: A symmetric matrix is a square matrix that is equal to its transpose (A = AT).
  5. Analyzing the given matrix: The given matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a diagonal matrix, but the diagonal elements are not equal. Therefore, it is not a scalar matrix or an identity matrix. It is also not a null matrix because the diagonal elements are non-zero. Since the matrix is diagonal, it is equal to its transpose, and hence it is a symmetric matrix.

Correct Answer: D<\/strong>

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an REMEMBER question because it requires recalling the definition of different types of matrices (scalar, identity, null, symmetric) and applying that knowledge to identify the given matrix.
Knowledge Dimension: FACTUAL
Justification: The question directly tests the knowledge of the definition of different types of matrices.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the understanding of matrix types as defined in the textbook.

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