A `3xx3` matrix given as, `a_(i j)=(i-j)/(i+2j)` cannot be expressed as a sum of symmetric and skew-symmetric matrix. True/False.

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 A=[a_(ij)] be a matrix of order 3xx3 where a_(ij) = (i-j)/(i+2j) cannot be expressed as a sum of symmetric and skew-symmetric matrix. Statement-2 Matrix A= [a_(ij)] _(nxxn),a_(ij) = (i-j)/(i+2j) is neither symmetric nor skew-symmetric.

Express A as the sum of a symmetric and a skew-symmetric matrix, where A=[(3,5),(-1,2)]

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and skew-symmetric matrix.

Express the matrix [{:(2 ,1),(3,4):}] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A = [{:(4, 2,-1),(3,5,7),(1,-2,1):} ] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A=[[3,-4], [1,-1]] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A=|(3, 2 ,3),(4,5 ,3),( 2, 4,5)| as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix B= [{:(,2,-2,),(,-1,3,):}] as the sum of a symmetric and a skew symmetric matrix.