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Diffstat (limited to 'FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py')
| -rw-r--r-- | FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py new file mode 100644 index 0000000..fb31881 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py @@ -0,0 +1,75 @@ +from manimlib.imports import * +class solution(LinearTransformationScene): + def construct(self): + + self.setup() + self.wait() + + o = TextMobject(r"This is the original $2D$ vector space(before Linear Transformation)") + o.move_to(DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + A = TextMobject("Let $A$ denote the matrix the of this linear transformation.") + A.move_to(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 i.e. a line ($1D$)") + o.move_to(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(DARK_BLUE) + arrow2.scale(1.2) + self.play(ShowCreation(arrow2)) + self.wait() + + o1 = TextMobject("If the vector lies in the transformed vector space") + o2 = TextMobject("(the line) then the solution exist") + o1.move_to(2*DOWN+2*RIGHT) + o2.move_to(2.5*DOWN+2*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(DARK_BLUE) + arrow1.scale(1.3) + self.play(ShowCreation(arrow1)) + self.wait() + + o1 = TextMobject("If the vector does lies in the transformed") + o2 = TextMobject("vector space then the does not solution exist") + o1.move_to(2*DOWN+2*RIGHT) + o2.move_to(2.5*DOWN+2*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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