Class CBSE Class 12 Mathematics Matrices and Determinants Q #762
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 MCQ SINGLE
Which of the following can be both a symmetric and skew-symmetric matrix ?
(A) Unit Matrix
(B) Diagonal Matrix
(C) Null Matrix
(D) Row Matrix
Prev Next
Correct Answer: C

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

  1. A symmetric matrix is a square matrix that is equal to its transpose (A = AT).

  2. A skew-symmetric matrix is a square matrix whose transpose is equal to its negative (AT = -A).

  3. Let's consider a matrix that is both symmetric and skew-symmetric. If A is both, then A = AT and AT = -A. Therefore, A = -A.

  4. This implies that all elements of A must be zero (aij = -aij, which means aij = 0 for all i and j).

  5. Therefore, the matrix must be a null matrix.

Correct Answer: Null Matrix

AI Suggestion: Option C

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to recall the definitions of symmetric and skew-symmetric matrices and apply that understanding to identify which matrix type can satisfy both conditions.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concepts of symmetric and skew-symmetric matrices, and how these properties relate to different types of matrices.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of matrix types and their properties as covered in the textbook.

More from this Chapter

MCQ_SINGLE
If \(F(x)=\begin{bmatrix}\cos~x&-\sin~x&0\\ \sin~x&\cos~x&0\\ 0&0&1\end{bmatrix}\) and \([F(x)]^{2}=F(kx)\), then the value of k is :
MCQ_SINGLE
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
MCQ_SINGLE
Sum of two skew-symmetric matrices of same order is always a/an:
MCQ_SINGLE
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
MCQ_SINGLE
If A=\begin{bmatrix}0&1\\ -1&0\end{bmatrix} and (3\~I+4\~A)(3\~I-4\~A)=x^{2}I, then the value(s) x is/are:
View All Questions