GATE BT 2015 • Q52 MCQ • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Fundamentals of Linear Algebra

Question Statement:

If matrix A = [[4, 2], [1, 3]], then the matrix resulting from the polynomial operation A^2 + 3A will be:

Options:

  • (A) [[30, 20], [10, 20]]
  • (B) [[28, 18], [9, 19]]
  • (C) [[32, 22], [11, 21]]
  • (D) [[25, 15], [8, 17]]

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2015 Q.52)** **1. Governing Concept & Syllabus Classification**: - **Section**: BT - **Question Type**: **MCQ** (2 Marks) - **Core Topic**: Biochemistry, Microbiology & Molecular Biology **2. Detailed Step-by-Step Analytical & Scientific Derivation**: - **Systematic Conceptual & Option-by-Option Evaluation**: - Problem Focus: *"If matrix A = [[4, 2], [1, 3]], then the matrix resulting from the polynomial operation A^2 + 3A will be:..."* - **Option (A) [CORRECT]**: *"[[30, 20], [10, 20]]"* - Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required. - **Option (B) [INCORRECT]**: *"[[28, 18], [9, 19]]"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (C) [INCORRECT]**: *"[[32, 22], [11, 21]]"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (D) [INCORRECT]**: *"[[25, 15], [8, 17]]"* does not satisfy the precise boundary conditions or molecular specificity. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **A** - **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).

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