Class CBSE Class 12 Mathematics Matrices and Determinants Q #1685
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
If $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$, then order of A must be:
(A) $3\times1$
(B) $1\times3$
(C) $1\times1$
(D) $3\times3$
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Correct Answer: B

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Detailed Solution

Step 1: Analyze the dimensions of the given matrices

Let the given equation be $X \cdot A = Y$. The matrix $X$ is a column matrix with 3 rows and 1 column, so its order is $3 \times 1$. The matrix $Y$ is a $3 \times 3$ matrix.

Step 2: Apply the rule of matrix multiplication

For the product $X \cdot A$ to be defined, the number of columns in $X$ must equal the number of rows in $A$. Since $X$ has 1 column, $A$ must have 1 row. Let the order of $A$ be $1 \times n$.

Step 3: Determine the dimensions of the product

The product of a $(3 \times 1)$ matrix and a $(1 \times n)$ matrix results in a matrix of order $(3 \times n)$. Given that the resulting matrix $Y$ is $(3 \times 3)$, we equate the dimensions: $3 \times n = 3 \times 3$. Therefore, $n = 3$.

Step 4: Conclusion

The order of matrix $A$ must be $1 \times 3$.

Final Answer: B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must utilize the fundamental rules of matrix multiplication dimensions to deduce the unknown order of a matrix.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the application of a specific algorithm/rule regarding matrix dimension compatibility rather than simple recall of definitions.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question tests the conceptual understanding of matrix algebra properties, which is a core competency in the Matrices chapter.

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