If C is a 5 x 1 matrix and D is a 3 x 5 matrix, what are the dimensions of DC?

Question

If C is a 5 x 1 matrix and D is a 3 x 5 matrix, what are the dimensions of DC?

Answer 1

3 x 1. A simple way I remember it is to put the sizes of the matrices you're multiplying in the order of the multiplication. For example, this one would be 3x5*5x1. For it to be possible to even multiply the matrices together, the middle numbers must match (they do -- 5) and the dimension of the resulting matrix is the outer numbers -- 3 x 1.