GATE BT 2015 • Q39
MCQ • 2 Marks
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Fundamentals of Linear Algebra
Question Statement:
What are the eigenvalues of the following matrix?
Lz 41
Options:
-
(A) 2 and 3
-
(B) -2 and 3
-
(C) 2 and -3
-
(D) -2 and -3
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2015 Q.39)**
**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: *"What are the eigenvalues of the following matrix?
Lz 41..."*
- **Option (A) [CORRECT]**: *"2 and 3"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"-2 and 3"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"2 and -3"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"-2 and -3
Options :
1. V A
2. * B
3.
4. * D"* 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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