math Problem.. Please help!!

Question

Obtain the 3x3 transformation matrix that first scales a two-dimensional object by

a factor of 2 in the x-direction and then reflects the modified object in the y-axis

and finally translates the object by 4 in the x-direction and -3 in the y-direction?

Answer 1

Suppose [a;b;c] is a point on the object with x-ccord a and y-coord b and z-coord c.

Scaling in the x-direction by a factor of two is done by the matrix

A1 = [2,0,0;0,1,0;0,0,1].

Reflection about the y-axis is done by negating the x-coordinate. So this matrix is

A2 = [-1,0,0;0,1,0;0,0,1].

Translation, however, is not a linear transformation; it requires vector addition. So, I would say the complete transformation is the function y given by

y(x) = A2*A1*x+[4;-3;0].