Class CBSE Class 12 Mathematics Matrices and Determinants Q #839
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If A=\begin{bmatrix}3&4\\ 5&2\end{bmatrix} and 2A+B is a null matrix, then B is equal to :
(A) \begin{bmatrix}6&8\\ 10&4\end{bmatrix}
(B) \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}
(C) \begin{bmatrix}5&8\\ 10&3\end{bmatrix}
(D) \begin{bmatrix}-5&-8\\ -10&-3\end{bmatrix}
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Step-by-Step Solution

Given: A = \begin{bmatrix}3&4\\ 5&2\end{bmatrix} and 2A + B = 0 (null matrix)

First, calculate 2A:

2A = 2 * \begin{bmatrix}3&4\\ 5&2\end{bmatrix} = \begin{bmatrix}6&8\\ 10&4\end{bmatrix}

Since 2A + B = 0, we can write B = -2A

Therefore, B = - \begin{bmatrix}6&8\\ 10&4\end{bmatrix} = \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}

Correct Answer: \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of matrix operations (scalar multiplication and null matrix) to find the matrix B.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (scalar multiplication and matrix subtraction) to arrive at the solution.
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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