Question Statement:
For a real symmetric matrix [A], which of the following statements is true:
Options:
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(A) The matrix is always diagonalizable and invertible.
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(B) The matrix is always invertible but not necessarily diagonalizable.
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(C) The matrix is always diagonalizable but not necessarily invertible.
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(D) The matrix is always neither diagonalizable nor invertible.
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2014 Q.1)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Verbal & Numerical Aptitude** under *General Aptitude* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Verbal & Numerical Aptitude.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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