Class CBSE Class 12 Mathematics Matrices and Determinants Q #838
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If for a square matrix A, A^{2}-3A+I=O and A^{-1}=xA+yI, then the value of x+y is:
(A) \-2
(B) 2
(C) 3
(D) -3
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Step-by-Step Solution

Given: A2 - 3A + I = O

Multiply both sides by A-1:

A-1(A2 - 3A + I) = A-1O

A-1A2 - 3A-1A + A-1I = O

A - 3I + A-1 = O

Rearrange to find A-1:

A-1 = 3I - A

Given: A-1 = xA + yI

Comparing the two expressions for A-1:

xA + yI = 3I - A

xA + yI = -A + 3I

By comparing coefficients:

x = -1

y = 3

Therefore, x + y = -1 + 3 = 2

Correct Answer: 2

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 concepts of matrix algebra, including the properties of the inverse of a matrix, to solve for the unknowns x and y.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to find the inverse of the matrix and then solve for the unknowns. This involves algebraic manipulation and application of matrix properties.
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 algebra concepts as covered in the textbook.

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