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from manimlib.imports import *
class Subspace_Example(Scene):
def construct(self):
sq = Square(side = 2, color=BLACK).shift(2*LEFT)
sq.set_fill(color=RED,opacity=350)
line1=Line(color=BLACK).shift(2*LEFT)
line1.rotate(np.pi/2)
line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
line2.scale(0.5)
line3=Line(color=BLACK).shift(+1.5*LEFT)
line3.scale(0.5)
a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
big_rect=Rectangle().scale(3).shift(0.5*DOWN)
big_rect.set_fill(color=GREY,opacity=350)
vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)
sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)
self.play(ShowCreation(vec_space))
self.play(ShowCreation(big_rect),ShowCreation(sub))
self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
rec.rotate(np.pi/2)
rec.set_fill(color=BLUE,opacity=350)
line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
self.wait(1)
text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
self.play(ShowCreation(text1),ShowCreation(text2))
self.wait(3)
self.play(FadeOut(text1),FadeOut(text2))
rec.shift(3*LEFT+2.01*DOWN)
line4.shift(3*LEFT+2*DOWN)
line5.shift(3*LEFT+2*DOWN)
line6.shift(3*LEFT+2*DOWN)
b1.shift(3.1*LEFT+2.1*DOWN)
b2.shift(3.1*LEFT+2.1*DOWN)
b3.shift(2.9*LEFT+2*DOWN)
b4.shift(2.9*LEFT+2.3*DOWN)
self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
self.wait(2)
text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
self.play(ShowCreation(text3),ShowCreation(text4))
self.wait(3)
rec.set_fill(color=GREY,opacity=350)
self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
sq1.set_fill(color=RED,opacity=350)
sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
sq2.set_fill(color=RED,opacity=350)
rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
rec1.set_fill(color=RED,opacity=350)
rec2=Rectangle(height=1.5,width=1,color=BLACK)
rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
self.wait(2.3)
text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
self.wait(3)
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