General Matrix Transformation

e_5 = 0

e_6 = 0

t_3 = 1

t_1 = 0 (slider from -10 to 10, step 0.1)
A = (2.0291326627212802, 6.633544994523059)
e_1 = 1 (slider from -5 to 5, step 0.1)
e_2 = 0 (slider from -5 to 5, step 0.1)
e_3 = 0 (slider from -5 to 5, step 0.1)
e_4 = 1 (slider from -5 to 5, step 0.1)
m: {{e_1, e_2}, {e_3, e_4}}
B = (6.919226662721275, 4.495958994523058)
C = (6.22817146272128, 2.106547794523061)
D = (5.762011462721279, 3.5315837945230584)
E = (0.9134884627212774, 4.039159794523061)
poly1, a, b, c, d, e = Polygon(A, B, C, D, E)
matrix1: m * poly1
B': m * B
C': m * C
D': m * D
E': m * E
A': m * A
poly2, a', e', d', c', b' = Polygon(A', E', D', C', B')
t_2 = 0 (slider from -10 to 10, step 0.1)
A'_x: e_1 * x(A) + e_2 * y(A) + t_1
A'_y: e_3 * x(A) + e_4 * y(A) + t_2
A'_t: (A'_x, A'_y)
B'_x: e_1 * x(B) + e_2 * y(B) + t_1
B'_y: e_3 * x(B) + e_4 * y(B) + t_2
C'_x: e_1 * x(C) + e_2 * y(C) + t_1
C'_y: e_3 * x(C) + e_4 * y(C) + t_2
D'_x: e_1 * x(D) + e_2 * y(D) + t_1
D'_y: e_3 * x(D) + e_4 * y(D) + t_2
E'_x: e_1 * x(E) + e_2 * y(E) + t_1
E'_y: e_3 * x(E) + e_4 * y(E) + t_2
B'_t: (B'_x, B'_y)
C'_t: (C'_x, C'_y)
D'_t: (D'_x, D'_y)
E'_t: (E'_x, E'_y)
poly3, a'_1, b'_1, c'_1, d'_1, e'_1 = Polygon(A'_t, B'_t, C'_t, D'_t, E'_t)
text1: "\begin{bmatrix}x'\\y'\\1\end{bmatrix}=\begin{bmatrix}" + (LaTeX[e_1]) + "&" + (LaTeX[e_2]) + "&" + (LaTeX[t_1]) + "\\" + (LaTeX[e_3]) + "&" + (LaTeX[e_4]) + "&" + (LaTeX[t_2]) + "\\" + (LaTeX[0]) + "&" + (LaTeX[0]) + "&" + (LaTeX[1]) + "\end{bmatrix}\begin{bmatrix}x\\y\\1\end{bmatrix}\"