MathDB

M = (a_{i,j} ), \ i, j = 1, 2, 3, 4

, is a square matrix of order four. Given that:
[*] (i) for each

i = 1, 2, 3,4

and for each

k = 5, 6, 7

a_{i,k} = a_{i,k-4};

P_i = a_{1,}i + a_{2,i+1} + a_{3,i+2} + a_{4,i+3};

S_i = a_{4,i }+ a_{3,i+1} + a_{2,i+2} + a_{1,i+3};

L_i = a_{i,1} + a_{i,2} + a_{i,3} + a_{i,4};

C_i = a_{1,i} + a_{2,i} + a_{3,i} + a_{4,i},

* for each

i, j = 1, 2, 3, 4

P_i = P_j , S_i = S_j , L_i = L_j , C_i = C_j

, and *

a_{1,1} = 0, a_{1,2} = 7, a_{2,1} = 11, a_{2,3} = 2

, and

a_{3,3} = 15

.
find the matrix M.

Problem Statement