The GATE Grind

GATE 2021 ST – Question 39

Matrix Theory · Inner Products and Quadratic Forms · 2 marks · Multiple choice

Let M be all symmetric positive definite real 3×3 matrices,and S={A∈M:A⁵⁰−A⁴⁸/4=0}. How many elements are in S?

  1. 0
  2. 1
  3. 8
  4. Infinitely many

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 1

Explanation

A is invertible,so multiply by A⁻⁴⁸ to get A²=I/4. Every eigenvalue is positive and solves λ²=1/4,hence equals 1/2. Symmetric diagonalization then forces A=I/2. Exactly **one, B**.

More Inner Products and Quadratic Forms questions

All Inner Products and Quadratic Forms questions →