Another math question?

Question

This is btw me and my brother. He thinks he knows it all and I don't know anything.

Also got another one:
A matrix is said to be stochastic if the row sum is equal to one. If you were to complete the matrix to the left so that each row, column, and 3 by 3 sub matrix (only nine used) contains every digit 1-9 what would you need to divide each element in the matrix by to make the 9 by 9 stochastic?

I am so tired now I have working on this for about 4-5 hours now!

Answer 1

At first I thought you'd need to have posted the matrix in order to be able to answer this question.

But...your description says that every row uses each digit from 1 to 9.

That means that every row must have the sum:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

So to make the sum of every row add up to 1, just divide every element in the matrix by 45.

(PS -- your description of the problem sounds like the matrix also would be a legal sudoku board.)