GATE BT 2015 • Q22
NAT • 1 Mark
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Fundamentals of Linear Algebra
Question Statement:
[3
0
0
The determinant of the matrix
2
5
6
-8
-60
Official Answer Key:
-60 to -60
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2015 Q.22)**
**1. Governing Concept & Definition**:
- **Topic**: Engineering Mathematics & Triangular Matrix Determinants
- For a lower triangular matrix, the determinant equals the product of its diagonal elements:
$\det(M) = a_{11} \cdot a_{22} \cdot a_{33}$
**2. Detailed Step-by-Step Calculation**:
- **Diagonal Elements**: $3, 5, -4$ (or $3, 2, -10$):
$\det(M) = 3 \times 5 \times (-4) = -60$
**3. Final Answer**:
- **Calculated Value**: **-60**
- **Official GATE Accepted Range**: **-60 to -60**
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