Class CBSE Class 12 Mathematics Matrices and Determinants Q #753
KNOWLEDGE BASED
REMEMBER
1 Marks 2025 MCQ SINGLE
If \(A=\begin{bmatrix}-1&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then A is a/an:
(A) scalar matrix
(B) identity matrix
(C) symmetric matrix
(D) skew-symmetric matrix
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Step-by-Step Solution

  1. Definition of Scalar Matrix: A scalar matrix is a diagonal matrix where all diagonal elements are equal.
  2. Definition of Identity Matrix: An identity matrix is a diagonal matrix where all diagonal elements are 1.
  3. Definition of Symmetric Matrix: A symmetric matrix is a square matrix that is equal to its transpose (A = AT).
  4. Definition of Skew-Symmetric Matrix: A skew-symmetric matrix is a square matrix that is equal to the negative of its transpose (A = -AT).
  5. Analyzing the given matrix A: The matrix A is a diagonal matrix with diagonal elements -1, 3, and 5. Since the diagonal elements are not all equal, it is not a scalar matrix. Since the diagonal elements are not all 1, it is not an identity matrix.
  6. Checking for Symmetric Property: The transpose of A (AT) is the same as A, so A = AT. Thus, A is a symmetric matrix.
  7. Checking for Skew-Symmetric Property: For A to be skew-symmetric, A must be equal to -AT. However, this is not the case here.

Correct Answer: symmetric matrix

AI Suggestion: Option C

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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.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of different types of matrices, such as scalar, identity, symmetric, and skew-symmetric matrices.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses knowledge of matrix types as defined in the textbook.

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