Let A be a m * p matrix whose columns all add to the same total s; and B be a p * n matrix whose columns all add to the same total t: Using summation notation prove that the n columns of AB each total st:
Let A be a m * p matrix whose columns all add to the same total s; and B be a p * n matrix whose columns all add to the same total t: Using summation notation prove that the n columns of AB each total st:
By definition of matrix multiplication, the entries of are given by .
We seek the sum of an arbitrary column of , given by
Thanks, what i was doing was expressing one column in Matrix A, by the sum of all columns divided by p, which was making it difficult to then simplify the expression for AB.