Question

Help me guys... Plz tell me about symmetric and skew -symmetric matrices.... ​

Answer 1

Answer:

Step-by-step explanation:A square matrix A is said to be symmetric if aij = aji for all i and j, where aij is an element present at (i,j)th position (ith row and jth column in matrix A) and aji is an element present at (j,i)th position (jth row and ith  column in matrix A). In other words, we can say that matrix A is said to be symmetric if the transpose of matrix A is equal to matrix A itself (AT=A). Let’s take an example of a matrix,

Symmetric Matrix

It is symmetric matrix because aij = aji for all i and j. Here, a12 = a21= 3, a13 = a31= 8 and a23 = a32 = -4 In other words, the transpose of Matrix A is equal to Matrix A itself (AT=A) which means matrix A is symmetric.

Skew-Symmetric Matrix

Square matrix A is said to be skew-symmetric if aij =−aji for all i and j. In other words, we can say that matrix A is said to be skew-symmetric if transpose of matrix A is equal to negative of matrix A i.e (AT =−A). Note that all the main diagonal elements in the skew-symmetric matrix are zero. Let’s take an example of a matrix

Symmetric Matrix

It is skew-symmetric matrix because aij =−aji for all i and j. Here, a12 = -6 and a21= -6 which means  a12= −a21. Similarly, this condition holds true for all other values of i and j.