Class CBSE Class 12 Mathematics Matrices and Determinants Q #728
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
If \(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\ -1\\ x\end{bmatrix}=\begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\ x\end{bmatrix},\) then value of x is:
(A) -1
(B) 0
(C) 1
(D) 2
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AI Tutor Explanation

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Step-by-Step Solution

First, perform the matrix multiplication on both sides of the equation:

\(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\ -1\\ x\end{bmatrix} = [5x - 2 + 0] = [5x - 2]\)

\(\begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\ x\end{bmatrix} = [-6 + x]\)

Now, equate the results:

\(5x - 2 = -6 + x\)

Solve for x:

\(5x - x = -6 + 2\)

\(4x = -4\)

\(x = -1\)

Correct Answer: -1

AI Suggestion: Option A

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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 sequence of steps involving matrix multiplication and algebraic manipulation 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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