Question

difference between symmetric and skew symmetric matrix class 12 maths

Answer 1

symmetric matrix are those matrix whose transpose is same as original matrix.

Skew symmetric matrix are those matrix, in which after transpose, -1 will has to be taken outside to attain the same matrix.

Answer 2

Difference between symmetric and skew symmetric matrix is explained below.

Step-by-step explanation:

Symmetric Matrix:

If the transpose of a matrix is equal to the matrix itself then the matrix is called a symmetric matrix.

mathematically,  for a matrix A, we can write:

$A^T=A$

Skew - Symmetric Matrix:

If the transpose of a matrix is equal to the negative of the matrix itself then the matrix is called a skew - symmetric matrix.

mathematically,  for a matrix A, we can write:

$A^T=-A$

The main diagonal elements of a skew symmetric matrix is zero.

#Learn More:

If the matrix A is both symmetric and skew-symmetric, show that A is a

zero matrix

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