Duduli

A square matrix will be called symmetric, if for all values of i & j ,      aij = aji i.e  A' = A Where A' is the transpose of matrix A e.g  

The rank of a matrix is said to be r if (a) It has at least one non-zero minor of order r. (b) Every minor of A of order higher than r is zero. Rank = Number of non-zero row in upper triangular matrix.

A matrix ‘A’ wil be called a periodic matrix, if,          A^k+1 = A        Where, K is a positive integer        If K is least positive integer then k is period of A If,     K=1 then A²=A which is idempotent matrix.      

A square matrix, all of whose elements below the leading diagonal are zero, is called an upper triangular matrix. A square matrix, all of whose elements above the leading diagonal are zero, is called a lower triangular matrix. e.g

Answer:- A square matrix A is called singular if determinant of A =0.If determinant of A≠0 then the matrix A is called a non-singular matrix or a regular matrix.

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