How can I reverse a coded message using a transformation matrix?

[gtfitzpatrick]

Homework Statement

in coding a msg, a black space was represented by 0, an A by 1,a B by 2 etc...The msg was transformed using the matrix

-1 -1 2 0
1 1 -1 0
0 0 -1 1
1 0 0 -1

and sent out as -19,19,25,-21,0,18,-18,15,3,10,-8,3,-2,20,-7,12

so what I've tried is...

so to reverse the transform i think i get the inverse of the transform matrix and multiply by the outputed answer

for the inverse i got

1 1 1 1
0 1 -1 -1
1 1 0 0
1 1 1 0

and multiplied it by
-19 19 25 -21
0 18 -18 15
3 10 -8 3
-2 20 -7 12

and got

-18 67 -8 9
-1 -12 -3 0
-19 37 7 -6
-16 47 -1 -3

which i was just going to convert back into letters to get the msg,but what letter is 67 or 37...Confussed...

 

[Dick]

You aren't supposed to multiply the inverse by the matrix of all of the integers in the message, you are supposed to multiply it by each of the column vectors [-19,19,25,-21]^T, [0,18,-18,15]^T etc. You could also transpose your data matrix.

 

[gtfitzpatrick]

thats dick, i'd just figured it out, i was just putting the coded msg in the wrong way round---the msg reads - do your homework-very good