GATE 2014 EC (EC2) – Question 38
Find the maximum determinant of a real symmetric 2 × 2 matrix with trace 14.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 48.9 to 49.1
Explanation
Real symmetry gives real eigenvalues λ1andλ2 with sum14. Their product is λ1(14−λ1)=49−(λ1−7)²≤49. Equality is attained by the matrix7I. Hence the maximum determinant is **49**, without needing a positive-definiteness assumption.