Question Statement:
For the matrix A = [a b
c d], if the relation a + b = c + d holds and a, b, c, d ≠ 0,
then which one of the following statements about A is FALSE?
Options:
-
(A) [1
1] is an eigenvector
-
(B) 𝜆 = a + b is an eigenvalue
-
(C) 𝜆 = d - b is an eigenvalue
-
(D) 𝜆 = d + b is an eigenvalue
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.37)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (2 Marks, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Linear Algebra & Differential Equations.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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