Hello
I would like to have help solving the problem:
I have to invent a marix 3*3 with entries from 1 to 8 such that all rows and all columns and al diagonals add to 12
the first row must be 7,2,3
thank you
i don't want the answer i want an explanation on how to get it
hehe no way u can solve this matrice..try it
look i got the answer and it seems that i don't need a proof of it..but what i need to prove is that:
is the matrix found unique?or is there other(s) matrices...so if u could solve the system u told me about,i think i can prove that it is unique
thank you
Sure, the easiest way is to start with the system and solve equation by equation for a variable
so from the first two
, , and keeping going like this solving for a new unknown (and substituting what you know). At the end you'll come up with a single equation for the last unknown and you'll know all the variables.
An interesting variation: Find all 3 X 3 matrices such that all the rows, columns and diagonals add up to the same number n and is this matrix unique?