Class CBSE Class 12 Mathematics Matrices and Determinants Q #734
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
\(If\begin{bmatrix}a&c&0\\ b&d&0\\ 0&0&5\end{bmatrix}\) is a scalar matrix, then the value of \(a+2b+3c+4d\) is:
(A) 0
(B) 5
(C) 10
(D) 25
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AI Tutor Explanation

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Step-by-Step Solution

  1. A scalar matrix is a diagonal matrix where all the diagonal elements are equal. Therefore, for the given matrix to be a scalar matrix, we must have \(a = d = 5\) and \(b = c = 0\).

  2. Substitute these values into the expression \(a + 2b + 3c + 4d\):

    \(a + 2b + 3c + 4d = 5 + 2(0) + 3(0) + 4(5)\)

  3. Simplify the expression:

    \(5 + 0 + 0 + 20 = 25\)

Correct Answer: 25

AI Suggestion: Option D

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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 the variables and then perform a calculation.
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 understanding and application of the definition of a scalar matrix, which is a textbook concept.

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