Page 3b -- Properties of Vector Algebra
Vectors can be expressed as rows or columns, but are most commonly in column vector format for ease of manipulation.
ADDITION:
An element in C is the sum of the corresponding elements in A and B. (Vectors must be the same size.)
MULTIPLICATION:
An element in C is the sum of the product of the corresponding row in A and column in B. The size of the resulting matrix is determined by the number of columns in A and rows in B.
For example: