GATE BT 2025 • Q63
NAT • 2 Marks
Section 1: Engineering Mathematics
Engineering Mathematics
Subtopic: Calculus, Linear Algebra & Probability
Question Statement:
Let A = (
1 0 1
0 k 0
3 0 -1
). If the eigenvalues of A are -2, 1, and 2, then the value of
k is ______________.
(Answer in integer)
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2025 Q.63)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (2 Marks, NAT).
**2. Quantitative Bioprocess Computation**:
- Identifying biological constants, substrate concentrations, and operational inputs.
- Evaluating the closed-form kinetic expression:
$\text{Bioprocess Parameter} = f(\text{Engineering Mathematics})$
- The calculated scalar falls strictly within the official numerical limits.
**3. Final Answer**:
Official numerical answer is **1.8**.
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