A good answer might be:

Yes, the dimensions are compatible:

Row Matrix times Matrix
as Several Dot Products

From the answer, you can see that row matrix times matrix is done by forming several dot products. However, here it is the columns of the matrix that get flipped:



QUESTION 10:

Is this type of product possible: 

Matrix  x  Row Matrix   =   ?

3 x 4        1 x  3     =   ?