Zaymiey

📐 Mathematics  ·  Matrices  ·  JEE

The eigenvalues of a real symmetric matrix are always:

Answer: Real.

  • A Complex conjugates
  • B Real
  • C Positive only
  • D Zero

Correct answer: B. Real

Explanation: Proof sketch: if Av = λv with v≠0, take conjugate transpose - v*A = λ̄v*. Then v*Av = λ̄(v*v). But also v*Av = λ(v*v), so λ = λ̄, meaning λ is real. Answer: Real.

Matrix A (3 rows x 3 columns)a11a12a13a21a22a23a31a32a33column 1column 2column 3row 1row 2row 3

Element aij of matrix A sits at the intersection of row i and column j.

Concept context

Matrix operations, determinants, inverses, and solving linear systems

Read the full Matrices notes →