Class CBSE Class 12 Mathematics Matrices and Determinants Q #765
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If
\[
A = \begin{pmatrix}
7 & 0 & x \\
0 & 7 & 0 \\
0 & 0 & y
\end{pmatrix}
\]
is a scalar matrix, then \(y^x\) is equal to
(A) \(0\)
(B) \(1\)
(C) \(7\)
(D) \(\pm 7\)
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Correct Answer: B
Explanation
A scalar matrix is a diagonal matrix where all the elements on the main diagonal are equal, and all non-diagonal elements are zero.

Here \(x=0\) and \(y=7\), So \(y^x\) is equal to 1

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Step-by-Step Solution

  1. A scalar matrix is a diagonal matrix where all the diagonal elements are equal.

  2. Given the matrix \(A = \begin{pmatrix} 7 & 0 & x \\ 0 & 7 & 0 \\ 0 & 0 & y \end{pmatrix}\), for it to be a scalar matrix, the off-diagonal elements must be zero, and the diagonal elements must be equal.

  3. Therefore, \(x = 0\) and \(y = 7\).

  4. Now, we need to find the value of \(y^x\), which is \(7^0\).

  5. Any non-zero number raised to the power of 0 is 1. Therefore, \(7^0 = 1\).

Correct Answer: 1

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 definition of a scalar matrix to determine the values of x and y, and then compute \(y^x\).
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of a scalar matrix and its properties to solve the problem.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of matrix types, specifically scalar matrices, which is a textbook definition.

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