GATE BT 2026 • Q41
MCQ • 2 Marks
Section 1: Engineering Mathematics
Engineering Mathematics
Subtopic: Calculus, Linear Algebra & Probability
Question Statement:
For the given matrix, which of the statements given below is/are true?
[
3 1 5
2 -1 0
5 2 9
]
Options:
-
(A) The matrix is full rank
-
(B) The matrix is invertible
-
(C) The matrix has a determinant
-
(D) The matrix has a transpose
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2026 Q.41)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Engineering Mathematics.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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