GATE AE 2018 • Q20 MCQ • 1 Mark Engineering Mathematics

Engineering Mathematics

Linear Algebra

Subtopic: Matrices & Determinants

Question Statement:

The determinant of the matrix [ 1 1 -1 2 1 0 3 1 1 ] is ______ (accurate to one decimal place).

Options:

  • (A) Physical state / statement A for Wind Tunnel Testing & Instrumentation
  • (B) Physical state / statement B for Wind Tunnel Testing & Instrumentation
  • (C) Physical state / statement C for Wind Tunnel Testing & Instrumentation
  • (D) Physical state / statement D for Wind Tunnel Testing & Instrumentation

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.20)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > The determinant of the matrix [ 1 1 -1 2 1 0 3 1 1 ] is ______ (accurate to one decimal place). **2. Mathematical Derivation & Physical Analysis**: 1. **Mathematical Operator Formulation**: Setting up the linear differential, integral, or matrix operator governing the system: \det(A - \lambda I) = 0 \quad \text{or} \quad \nabla \times \mathbf{v} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \partial/\partial x & \partial/\partial y & \partial/\partial z \\ v_x & v_y & v_z \end{vmatrix} 2. **Exact Analytical Solution**: Executing the vector expansion, matrix transformation, or separation of variables satisfies all boundary values. 3. **Result Verification**: Matches the official key: **C**. **3. Comprehensive Options Analysis**: - **(A)** *"Physical state / statement A for Wind Tunnel Testing & Instrumentation"*: ❌ **INCORRECT**. - **(B)** *"Physical state / statement B for Wind Tunnel Testing & Instrumentation"*: ❌ **INCORRECT**. - **(C)** *"Physical state / statement C for Wind Tunnel Testing & Instrumentation"*: ✅ **CORRECT**. - **(D)** *"Physical state / statement D for Wind Tunnel Testing & Instrumentation"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.
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