Question Bank • QB_EM_GATE_001
MCQ • 2 Marks
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Eigen values and Eigen vectors
Question Statement:
Match the Matrix Types in Group-I with their corresponding Eigenvalue Characteristics in Group-II:
$\begin{array}{|ll|ll|}\hline \textbf{Group-I (Matrix)} & & \textbf{Group-II (Eigenvalues)} & \\ \hline \text{P. Real Symmetric Matrix} & & \text{1. Modulus } |\lambda| = 1 \\ \text{Q. Real Skew-Symmetric Matrix} & & \text{2. Strictly real} \\ \text{R. Real Orthogonal Matrix} & & \text{3. Purely imaginary or zero} \\ \text{S. Idempotent Matrix } (A^2 = A) & & \text{4. Only 0 or 1} \\ \hline \end{array}$
Choose the CORRECT matching combination:
Options:
-
(A) P-2, Q-3, R-1, S-4
-
(B) P-3, Q-2, R-4, S-1
-
(C) P-2, Q-1, R-3, S-4
-
(D) P-4, Q-3, R-1, S-2
Step-by-Step Solution & Explanation
Analysis of Eigenvalue Properties:
- **P. Real Symmetric Matrix**: All eigenvalues are strictly **real** (P-2).
- **Q. Real Skew-Symmetric Matrix**: Eigenvalues are either **purely imaginary or zero** (Q-3).
- **R. Real Orthogonal Matrix**: Modulus $|\lambda| = 1$ (R-1).
- **S. Idempotent Matrix**: $\lambda^2 = \lambda \implies \lambda \in \{0, 1\}$ (S-4).
Correct matching: **P-2, Q-3, R-1, S-4**.
Practice In Authentic CBT Exam Interface
Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.
Launch CBT Mock Test