Express the matrix as the sum of a symmetric and skew-symmetric matrix and verify your result.

If find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = O.

If and B = [1 0 4], verify that (AB)^T = B^TA^T.

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways; telephone, house calls and letters. The cost per contact (in paise) is given matrix A as

The number of contacts of each type made in two cities X and Y is given in matrix B as

Find the total amount spent by the group in the two cities X and Y.

If then prove by principle of mathematical induction that for all n ∈ N.