GATE BT 2012 • Q32 MCQ • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Fundamentals of Linear Algebra

Question Statement:

What is the rank of the following matrix? 5 3 1 6 2 4 14 10 0    (A) 0 (B) 1 (C) 2 (D) 3

Options:

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2012 Q.32)** **1. Governing Concept & Syllabus Classification**: - **Section**: BT - **Question Type**: **MCQ** (2 Marks) - **Core Topic**: Engineering Mathematics **2. Detailed Step-by-Step Analytical & Scientific Derivation**: - **Systematic Conceptual & Option-by-Option Evaluation**: - Problem Focus: *"What is the rank of the following matrix? 5 3 1 6 2 4 14 10 0   ..."* - **Option (C) [CORRECT]**: *"2"* - Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required. - **Option (A) [INCORRECT]**: *"0"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (B) [INCORRECT]**: *"1"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (D) [INCORRECT]**: *"3"* does not satisfy the precise boundary conditions or molecular specificity. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **C** - **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).

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