2 files changed, 91 insertions, 10 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
index b400f93..a5d96f5 100755
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
@@ -4,31 +4,37 @@ class Orthogonal(ThreeDScene):
     def construct(self):

         axes = ThreeDAxes()

         self.play(ShowCreation(axes))

-        self.move_camera(phi=30*DEGREES,theta=-45*DEGREES,run_time=3)

-        line1 = Line(start = ORIGIN,end = -3*LEFT)

+        self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3)

+

+        text = TextMobject(r"$\hat{i}$",r"$\hat{j}$",r"$\hat{k}$")

+        text[0].move_to(0.7*DOWN+0.8*LEFT)

+        text[1].move_to(0.75*DOWN+0.7*RIGHT)

+        text[2].move_to(0.75*UP+0.4*RIGHT)

+        self.add_fixed_in_frame_mobjects(text)

+        self.play(Write(text))

+

+        line1 = Line(start = ORIGIN,end = RIGHT)

         line1.set_color(DARK_BLUE)

-        tip1 = Polygon(-LEFT,-0.8*LEFT-0.2*DOWN,-0.8*LEFT-0.2*UP)

-        tip1.move_to(-3*LEFT)

+        tip1 = Polygon(-0.95*LEFT,-0.8*LEFT-0.1*DOWN,-0.8*LEFT-0.1*UP)

         tip1.set_opacity(1)

         tip1.set_fill(DARK_BLUE)

         tip1.set_color(DARK_BLUE)

 

-        arrow2 = Line(start = ORIGIN,end = -3*UP)

+        arrow2 = Line(start = ORIGIN,end = UP)

         arrow2.set_color(DARK_BLUE)

-        tip2 = Polygon(DOWN,0.8*DOWN-0.2*RIGHT,0.8*DOWN-0.2*LEFT)

-        tip2.move_to(3*DOWN)

+        tip2 = Polygon(0.95*UP,0.8*UP-0.1*RIGHT,0.8*UP-0.1*LEFT)

         tip2.set_opacity(1)

         tip2.set_fill(DARK_BLUE)

         tip2.set_color(DARK_BLUE)

         arrow2.set_color(DARK_BLUE)

 

-        arrow3 = Line(start = ORIGIN,end = [0,0,3])

+        arrow3 = Line(start = ORIGIN,end = [0,0,1])

         arrow3.set_color(DARK_BLUE)

-        tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*LEFT)

+        tip3 = Polygon([0,0,0.95],[0,0,0.8]-0.1*RIGHT,[0,0,0.8]-0.1*LEFT)

         tip3.set_opacity(1)

         tip3.set_fill(DARK_BLUE)

         tip3.set_color(DARK_BLUE)

 

         self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))

         

-        self.wait()
\ No newline at end of file
+        self.wait()

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