Thread: Linear algebra proof

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:

Originally Posted by ulysses123

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.