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from manimlib.imports import *
class RN_Line(LinearTransformationScene):
def construct(self):
self.setup()
self.wait()
predim = TextMobject("Dimension of this vector space is 2")
predim.move_to(DOWN+4*LEFT)
predim.scale(0.75)
predim.add_background_rectangle()
self.play(Write(predim))
self.wait()
self.play(FadeOut(predim))
afterlt = TextMobject("After Linear transformation")
afterlt.move_to(DOWN+4*LEFT)
afterlt.scale(0.75)
afterlt.add_background_rectangle()
afterlt2 = TextMobject("Dimension of the vector space","changes to 1")
afterlt2[0].move_to(1.5*DOWN+4*LEFT)
afterlt2[1].move_to(2*DOWN+4*LEFT)
afterlt2.scale(0.75)
afterlt2.add_background_rectangle()
matrix = [[1,1],[1,1]]
self.apply_matrix(matrix)
self.play(Write(afterlt))
self.play(Write(afterlt2))
self.wait()
nullity = TextMobject("Hence, nullity = 1")
nullity.move_to(DOWN+4*LEFT)
self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
self.wait(1)
self.play(FadeOut(nullity))
class RN_Point(LinearTransformationScene):
def construct(self):
self.setup()
self.wait()
predim = TextMobject("Another One")
predim.move_to(DOWN+4*LEFT)
predim.scale(0.75)
predim.add_background_rectangle()
self.play(Write(predim))
self.wait()
self.play(FadeOut(predim))
afterlt = TextMobject("After Linear transformation")
afterlt.move_to(DOWN+4*LEFT)
afterlt.scale(0.75)
afterlt.add_background_rectangle()
afterlt2 = TextMobject("Dimension of the vector space","changes to 0")
afterlt2[0].move_to(1.5*DOWN+4*LEFT)
afterlt2[1].move_to(2*DOWN+4*LEFT)
afterlt2.scale(0.75)
afterlt2.add_background_rectangle()
matrix = [[0,0],[0,0]]
self.apply_matrix(matrix)
self.play(Write(afterlt))
self.play(Write(afterlt2))
self.wait()
nullity = TextMobject("Hence, nullity = 2")
nullity.move_to(DOWN+4*LEFT)
self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
self.wait(1)
self.play(FadeOut(nullity))
class RN_SameDim(LinearTransformationScene):
def construct(self):
self.setup()
self.wait()
predim = TextMobject("Let us look at another example")
predim.add_background_rectangle()
predim.move_to(DOWN+4*LEFT)
predim.scale(0.75)
self.play(Write(predim))
self.wait()
self.play(FadeOut(predim))
afterlt = TextMobject("After Linear transformation")
afterlt.move_to(DOWN+4*LEFT)
afterlt.scale(0.75)
afterlt.add_background_rectangle()
afterlt2 = TextMobject("Dimension of the vector space","remains to be 2")
afterlt2[0].move_to(1.5*DOWN+4*LEFT)
afterlt2[1].move_to(2*DOWN+4*LEFT)
afterlt2.scale(0.75)
afterlt2.add_background_rectangle()
matrix = [[1,1],[0,1]]
self.apply_matrix(matrix)
self.play(Write(afterlt))
self.play(Write(afterlt2))
self.wait()
nullity = TextMobject("Hence, nullity = 0")
nullity.move_to(DOWN+4*LEFT)
self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
self.wait(1)
self.play(FadeOut(nullity))
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