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from manimlib.imports import *
class solution(LinearTransformationScene):
def construct(self):
self.setup()
self.wait()
o = TextMobject(r"This is the original vector space $R^2$ (before Linear Transformation)")
o.move_to(3*DOWN)
o.scale(0.75)
o.add_background_rectangle()
self.play(Write(o))
self.wait()
self.play(FadeOut(o))
A = TextMobject(r"Consider the matrix the of this linear transformation $A$ = $\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$")
A.move_to(3*DOWN)
A.scale(0.75)
A.add_background_rectangle()
self.play(Write(A))
matrix = [[1,-1],[1,-1]]
self.apply_matrix(matrix)
self.wait()
self.play(FadeOut(A))
o = TextMobject(r"This is the transformed vector space")
o.move_to(3*DOWN)
o.scale(0.75)
o.add_background_rectangle()
self.play(Write(o))
self.wait()
self.play(FadeOut(o))
arrow2 = Arrow(start = ORIGIN, end = 2*DOWN+2*LEFT)
arrow2.set_color(PURPLE)
arrow2.scale(1.2)
self.play(ShowCreation(arrow2))
self.wait()
o1 = TextMobject("If the ","vector b"," lies in the transformed vector space")
o2 = TextMobject("(the line) then the solution exist")
o1.move_to(2.5*DOWN+2*RIGHT)
o1[1].set_color(PURPLE)
o2.move_to(3*DOWN+2.5*RIGHT)
o1.scale(0.75)
o2.scale(0.75)
o1.add_background_rectangle()
o2.add_background_rectangle()
self.play(Write(o1))
self.play(Write(o2))
self.wait()
self.play(FadeOut(o1), FadeOut(o2))
self.play(FadeOut(arrow2))
arrow1 = Arrow(start = ORIGIN, end = 2*UP+RIGHT)
arrow1.set_color(ORANGE)
arrow1.scale(1.3)
self.play(ShowCreation(arrow1))
self.wait()
o1 = TextMobject("If the ","vector b"," does lies in the transformed")
o2 = TextMobject("vector space then the does not solution exist")
o1.move_to(2.5*DOWN+2*RIGHT)
o1[1].set_color(ORANGE)
o2.move_to(3*DOWN+2.5*RIGHT)
o1.scale(0.75)
o2.scale(0.75)
o1.add_background_rectangle()
o2.add_background_rectangle()
self.play(Write(o1))
self.play(Write(o2))
self.wait()
self.play(FadeOut(o1), FadeOut(o2))
self.play(FadeOut(arrow1))
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