Class CBSE Class 12 Mathematics Matrices and Determinants Q #837
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals
(A) ±1
(B) -1
(C) 1
(D) 2
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AI Tutor Explanation

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Step-by-Step Solution

First, we need to find B²:

B² = B * B = [(x, 0), (1, 1)] * [(x, 0), (1, 1)]

B² = [ (x*x + 0*1, x*0 + 0*1), (1*x + 1*1, 1*0 + 1*1) ]

B² = [(x², 0), (x+1, 1)]

Now, we are given that A = B²:

[(1, 0), (2, 1)] = [(x², 0), (x+1, 1)]

By comparing the elements of the matrices, we get the following equations:

1 = x²

2 = x + 1

From the second equation, we can solve for x:

x = 2 - 1

x = 1

Correct Answer: 1

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 equality to find the value of x.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure of matrix multiplication and comparison 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 of matrix operations as covered in the textbook.

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