When we multiply our Vector with These Transformation Matrix, we get Transformed Vector but order of multiplication is depend upon which type of matrix(row matrix or column matrix) represent our vector.These is shown in figure below.

Suppose we have one Triangle(A,B,C) and we want to Translate it By (2,2) then we have to multiply (A,B,C) with The Transformation Matrix of Translation.After Multiplication,we get Transformed(A,B,C) which is (A',B',C').Transformation matrix of translation and example of Triangle(A,B,C) is shown in figure below.

For any other Transformation,procedure for getting Transformed vector is same but Transformation Matrix for each Transformation differs.For more detailed information on each Transformations,please visit Documents page of this website.There you can see our YouTube video on Linear Transformation and Matrices. You can see images of different Transformations in the Image carousel given below.