file1_of orthonormal bases updated

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))
+        
\ No newline at end of file