Class CBSE Class 12 Mathematics Matrices and Determinants Q #730
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
Given that \([\begin{matrix}1&x\end{matrix}]\begin{bmatrix}4&0\\ -2&0\end{bmatrix}=0,\) the value of x is:
(A) -4
(B) -2
(C) 2
(D) 4
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AI Tutor Explanation

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Step-by-Step Solution

  1. First, perform the matrix multiplication: \[\begin{bmatrix}1&x\end{bmatrix}\begin{bmatrix}4&0\\ -2&0\end{bmatrix} = \begin{bmatrix}1(4) + x(-2) & 1(0) + x(0)\end{bmatrix} = \begin{bmatrix}4 - 2x & 0\end{bmatrix}\]
  2. We are given that the result is equal to 0: \[\begin{bmatrix}4 - 2x & 0\end{bmatrix} = \begin{bmatrix}0 & 0\end{bmatrix}\]
  3. This implies that \(4 - 2x = 0\).
  4. Solve for x: \(2x = 4\) \(x = \frac{4}{2}\) \(x = 2\)

Correct Answer: 2

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of matrix multiplication and solving equations to find the value of 'x'.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, namely matrix multiplication and then solving the resulting equation.
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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