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📐 Mathematics  ·  Matrices  ·  JEE

Every square matrix can be written uniquely as the sum of a symmetric matrix and a:

Answer: a skew-symmetric one.

  • A a skew-symmetric one
  • B a diagonal matrix
  • C a scalar matrix
  • D a null matrix

Correct answer: A. a skew-symmetric one

Explanation: A = ½(A + Aᵀ) + ½(A − Aᵀ), the sum of a symmetric and a skew-symmetric part.

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

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