Class CBSE Class 12 Mathematics Matrices and Determinants Q #844
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
4. If a matrix $A=\begin{bmatrix}1 & 2 & 3\end{bmatrix}$, then the matrix $AA'$ (where $A'$ is the transpose of A) is:
(A) 14
(B) $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
(C) $\begin{bmatrix}1 & 2 & 3\\ 2 & 3 & 1\\ 3 & 1 & 2\end{bmatrix}$
(D) $\begin{bmatrix}14\end{bmatrix}$
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Step-by-Step Solution

  1. Given matrix $A = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$.
  2. Find the transpose of A, denoted as $A'$. $A' = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$.
  3. Multiply A by A': $AA' = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} = (1 \times 1) + (2 \times 2) + (3 \times 3) = 1 + 4 + 9 = 14$.
  4. Represent the result as a 1x1 matrix: $\begin{bmatrix} 14 \end{bmatrix}$.

Correct Answer: $\begin{bmatrix}14\end{bmatrix}$

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of matrix transpose and matrix multiplication to find the result.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, specifically finding the transpose of a matrix and then performing matrix multiplication.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of matrix operations as covered in the textbook.

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