4 files changed, 109 insertions, 0 deletions
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
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+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
@@ -0,0 +1,9 @@
+# Contributer: Archit Sangal
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
+<br/></br>
+
+## Sub-Topics Covered:
++ The Rank-Nullity Theorem
+
+#### Video 1: Visually understanding linear transformation(using grid)
+![GIF1](file2.gif)
+\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
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+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
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+file 'RN_Line.mp4'
+file 'RN_Point.mp4'
+file 'RN_SameDim.mp4'
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
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+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
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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))
+\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif
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index 0000000..46efc66
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif