A matrix times a column matrix results in a column matrix.
Here is an example of a matrix times a column matrix:
The details of how this is done will be explained later. For now, look at the dimensions of the operands and of the result. A matrix times column matrix product can be formed if the dimensions look like this:
Matrix x Col. Matrix = Resulting Col. Matrix R x N N x 1 = R x 1 -------- same
For the above example:
Matrix x Col. Matrix = Resulting Col. Matrix 2 x 2 2 x 1 = 2 x 1 -------- same
Dimensions are displayed as "Row x Column". An R x 1 matrix is a column matrix (because it has 1 column).
What are the dimensions of the result, below:
Matrix x Col. Matrix = Resulting Col. Matrix 5 x 5 5 x 1 = ? x ?