REPRESENTING POINT AS ROW VECTOR vs. COLUMN VECTOR

There are two ways of representing a point in space either using Row Vector or using Column Vector

ROW MATRIX REPRESENTATION

COLUMN MATRIX REPRESENTATION

For row-matrix representation we form composite transformations by multiplying matrices in order from left to right whereas in column-matrix representation we form composite transformations by multiplying matrices in order from right to left. The transformation matrices depends on the way we represent a point for example if the point is represented using the Row-Matrix representation then the translation matrix can be written as:

whereas if the point is represented using the column-matrix representation then the translation matrix is transposed before multiplication as below: