Letting a "blank" = 0, A =1, B = 2, C= 3....etc., we can place the original message into the following 5 x 3 matrix
[ 15 14 5
0 9 6
0 2 25
0 12 1
14 4 0 ]
We then multiply this matrix by the encoding matrix
[ 15 14 5 [ 0 5 -5
0 9 6 5 -5 5
0 2 25 -5 5 0 ]
0 12 1
14 4 0 ]
And we get the following result.....call this Matrix "X"......this would be the matrix that we would send to our "receiver"
[ 45 30 -5
15 -15 45
-115 115 10
55 -55 60
20 50 -50 ]
Now..... for the receiver to decode this matrix, he needs to first find the inverese of the encoding matrix ......this is
[ 1/5 1/5 0
1/5 1/5 1/5
0 1/5 1/5 ]
Now.....multiplying Matrix "X" by the inverse of the encoding matrix [in that order] would reveal our original message matrix to the receiver
And....lo and behold!!!!!........ the result is
[ 15 14 5
0 9 6
0 2 25
0 12 1
14 4 0 ] our original message matrix !!!!!