Merge pull request #24 from architsangal/master

Updating Folder Name

16 files changed, 466 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt
new file mode 100644
index 0000000..cae98ce
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt
@@ -0,0 +1,3 @@
+file 'text.mp4'
+file 'LinearTransformation.mp4'
+file 'NonLinearTransformation.mp4'
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
new file mode 100644
index 0000000..677f890
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
@@ -0,0 +1,45 @@
+from manimlib.imports import *
+
+class text(Scene):
+    def construct(self):
+        text1 = TextMobject("For a grid, undergoing a linear transformation, all it's straight lines")
+        text1.scale(0.9)
+        text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed")
+        text2.scale(0.9)
+        text1.move_to(ORIGIN+UP)
+        text2.move_to(ORIGIN)
+        self.play(Write(text1))
+        self.play(Write(text2))
+        self.wait()
+        self.play(FadeOut(text1),FadeOut(text2))
+
+class LinearTransformation(LinearTransformationScene):
+    CONFIG = {
+    "basis_vector_stroke_width": 3,
+    "leave_ghost_vectors": True,
+    }
+
+    def construct(self):
+        self.setup()
+        matrix = [[0.866,-0.5],[0.5,0.866]]
+        self.apply_matrix(matrix)
+        text = TextMobject("This is a Linear","Trasformation")
+        text[0].move_to(DOWN+4*LEFT)
+        text[1].move_to(1.5*DOWN+4*LEFT)
+        text.add_background_rectangle()
+        self.play(Write(text))
+        self.wait()
+
+class NonLinearTransformation(Scene):
+    def construct(self):
+        grid = NumberPlane()
+        self.play(ShowCreation(grid),run_time =2)
+        NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,])
+        grid.prepare_for_nonlinear_transform()
+        self.play(grid.apply_function,NonLinearTrans)
+        text = TextMobject("While, this is not a","Linear Trasformation")
+        text[0].move_to(DOWN+4*LEFT)
+        text[1].move_to(1.5*DOWN+4*LEFT)
+        text.add_background_rectangle()
+        self.play(Write(text))
+        self.wait()
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py
index 577032d..577032d 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_Understand_Linear_Transformations_visually.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_Uniform_Scaling.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py
index a7856a5..a7856a5 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_Uniform_Scaling.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py
index 91f098e..91f098e 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif
index 9bef1b6..9bef1b6 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py
index 718e4e0..718e4e0 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif
index 7ca323f..7ca323f 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py
new file mode 100755
index 0000000..01a0cef
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py
@@ -0,0 +1,27 @@
+from manimlib.imports import *

+class LinearTrans(LinearTransformationScene,MovingCameraScene):

+        CONFIG = {

+        "basis_vector_stroke_width": 1,

+        "leave_ghost_vectors": True,

+        }

+

+        def setup(self):

+            LinearTransformationScene.setup(self)

+            MovingCameraScene.setup(self)

+        

+        def construct(self):

+            self.setup()

+            self.camera_frame.save_state()

+            self.play(self.camera_frame.set_width, 7)

+            matrix = [[0.866,-0.5],[0.5,0.866]]

+            self.apply_matrix(matrix)

+            arc1 = Arc(radius = 0.25,angle=TAU/12)

+            arc2 = Arc(radius = 0.25,angle=TAU/12,start_angle=TAU/4)

+            text1 = TextMobject(r"$\theta$")

+            text1.scale(0.5)

+            text1.move_to(0.5*UP+0.125*LEFT)

+            text2 = TextMobject(r"$\theta$")

+            text2.scale(0.5)

+            text2.move_to(0.5*RIGHT+0.125*UP)

+            self.play(ShowCreation(arc1),ShowCreation(arc2),Write(text1),Write(text2),run_time=1)

+            self.wait()

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
new file mode 100755
index 0000000..b400f93
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
@@ -0,0 +1,34 @@
+from manimlib.imports import *

+

+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)

+        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.set_opacity(1)

+        tip1.set_fill(DARK_BLUE)

+        tip1.set_color(DARK_BLUE)

+

+        arrow2 = Line(start = ORIGIN,end = -3*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.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.set_color(DARK_BLUE)

+        tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*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
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
new file mode 100644
index 0000000..0a28f22
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
@@ -0,0 +1,82 @@
+from manimlib.imports import *
+class OrthonormalBasis(GraphScene):
+    CONFIG = {
+        "x_min" : -6,
+        "x_max" : 6,
+        "y_min" : -4,
+        "y_max" : 4,
+        "graph_origin" : ORIGIN ,
+}
+
+    def construct(self):
+        self.setup_axes(animate=True)
+
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT)
+        arrow1.scale(2.25)
+        arrow1.set_color(DARK_BLUE)
+
+        arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT)
+        arrow2.scale(2.25)
+        arrow2.set_color(DARK_BLUE)
+
+        square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT))
+        square.set_color(DARK_BLUE)
+        self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square))
+
+        ortho = TextMobject("Orthonormal Vectors")
+        ortho.scale(0.75)
+        ortho.move_to(DOWN+3*RIGHT)
+        self.play(Write(ortho))
+        self.wait()
+        self.play(FadeOut(ortho))
+
+        arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT)
+        arrow3.scale(1.25)
+        arrow3.set_color(GOLD_E)
+        self.play(ShowCreation(arrow3))
+
+        arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT)
+        arrow4.scale(1.8)
+        arrow4.set_color(GOLD_A)
+        
+        arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT)
+        arrow5.scale(1.3)
+        arrow5.set_color(GOLD_A)
+        
+        self.play(ShowCreation(arrow5), ShowCreation(arrow4))
+        
+        self.wait()
+
+        self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square))
+
+        self.wait()
+
+        text1 = TextMobject(r"$<v,v_1> v_1$")
+        text1.move_to(UP+2*RIGHT)
+        text1.scale(0.75)
+        text2 = TextMobject(r"$<v,v_2> v_2$")
+        text2.move_to(UP+3*LEFT)
+        text2.scale(0.75)
+        
+        text3 = TextMobject("v")
+        text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT)
+
+        self.play(Write(text1), Write(text2), Write(text3))
+        self.wait()
+
+        line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT)
+        line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT)
+        self.play(ShowCreation(line1),ShowCreation(line2))
+
+        self.wait()
+        
+        text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors")
+        text[0].move_to(DOWN+3.2*RIGHT)
+        text[1].move_to(1.5*DOWN+3.2*RIGHT)
+        self.play(Write(text))
+        self.wait(2)
+        self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2))
+        self.play(FadeOut(text))
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif
new file mode 100644
index 0000000..7d8d2e1
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py
new file mode 100644
index 0000000..afe4f9a
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py
@@ -0,0 +1,30 @@
+from manimlib.imports import *
+
+class Column_Space(Scene):
+    def construct(self):
+
+        A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
+        A.move_to(2*UP)
+        A[1].set_color(color = DARK_BLUE)
+        A.scale(0.75)
+
+        self.play(Write(A),run_time = 1)      
+
+        CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$")
+        CS_A.move_to(1.5*LEFT+1*DOWN)
+        CS_A[1].set_color(color = DARK_BLUE)
+        CS_A[3].set_color(color = DARK_BLUE)
+        CS_A[5].set_color(color = DARK_BLUE)
+        CS_A.scale(0.75)
+
+        self.play(Write(CS_A),run_time = 2)
+
+        arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT)
+        arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT)
+        arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT)
+
+        Defn = TextMobject("Linear Combination of Columns of Matrix")
+        Defn.move_to(3*DOWN)
+
+        self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1)
+        self.wait(1)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py
new file mode 100644
index 0000000..b16a32a
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py
@@ -0,0 +1,145 @@
+from manimlib.imports import *
+
+class Row_Space(Scene):
+    def construct(self):
+
+        Heading = TextMobject("Row Space")
+        defn1 = TextMobject("Definition 1: Row Space of a matrix is the linear combination of the rows of that matrix.")
+        defn2 = TextMobject("Definition 2: It is a vector space generated by a linear combination of the columns of $A^{T}$.")
+        equivalent = TextMobject(r"Definition 1 $\equiv$ Definition 2")
+
+        Heading.move_to(2*UP)
+        Heading.set_color(color = DARK_BLUE)
+
+        defn1.move_to(UP)
+        defn1.scale(0.75)
+
+        defn2.scale(0.75)
+
+        equivalent.move_to(DOWN)
+
+        self.play(Write(Heading))
+        self.play(Write(defn1))
+        self.play(Write(defn2))
+        self.play(Write(equivalent))
+
+        self.wait(2)
+        self.play(FadeOut(Heading),FadeOut(defn1),FadeOut(defn2),ApplyMethod(equivalent.move_to,2*UP))
+
+        how = TextMobject("Let us see, How?")
+        how.move_to(UP)
+        self.play(Write(how))
+        self.play(FadeOut(equivalent),FadeOut(how))
+
+        A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
+        A.move_to(2*UP+3*LEFT)
+        A[1].set_color(color = DARK_BLUE)
+        A.scale(0.80)
+
+        self.play(Write(A))
+
+        rows = TextMobject(r"Rows of A $\rightarrow$",
+        r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$,",
+        r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$,",
+        r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$,",
+        r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$")
+        rows.scale(0.75)
+        rows[1:5].set_color(DARK_BLUE)
+        self.play(Write(rows))
+
+        ac_defn1 = TextMobject("According to Definition 1 : ")
+        ac_defn1.move_to(DOWN)
+
+        RS_A = TextMobject(r"Row Space of $A = x_{1}$",
+        r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$",
+        r"$+x_{2}$",
+        r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$",
+        r"$ + x_{3}$",
+        r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$",
+        r"$+x_{4}$",
+        r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$")
+        RS_A.move_to(DOWN+DOWN)
+        RS_A[6].move_to(2*DOWN+DOWN)
+        RS_A[7].move_to(2*DOWN+2*RIGHT+DOWN)
+        RS_A[1].set_color(color = DARK_BLUE)
+        RS_A[3].set_color(color = DARK_BLUE)
+        RS_A[5].set_color(color = DARK_BLUE)
+        RS_A[7].set_color(color = DARK_BLUE)
+        RS_A.scale(0.75)
+
+        self.play(FadeOut(rows[0]),Transform(rows[1],RS_A[1]),Transform(rows[2],RS_A[3]),Transform(rows[3],RS_A[5]),Transform(rows[4],RS_A[7]))
+        self.play(FadeIn(ac_defn1), Write(RS_A))
+        self.wait(1)
+
+        self.play(FadeOut(rows[1]), FadeOut(rows[2]), FadeOut(rows[3]), FadeOut(rows[4]), FadeOut(RS_A), FadeOut(ac_defn1))
+
+        A_T = TextMobject(r"$A^{T} = $",r"$\left( \begin{array}{c c c c} 1 & 1 & 2 & 3 \\ 2 & 3 & 1 & 2 \\ 1 & 1 & 4 & 3 \end{array} \right)$")
+        A_T.move_to(2*UP+3*RIGHT)
+        A_T[1].set_color(color = DARK_BLUE)
+        A_T.scale(0.80)
+
+        self.play(Write(A_T))
+
+        change1 = TextMobject(r"Rows of $A\equiv$ Columns of $A^{T}$")
+        change2 = TextMobject(r"Columns of $A\equiv$ Rows of $A^{T}$")
+        change2.move_to(DOWN)
+
+        change3 = TextMobject(r"Row Space of $A$ = Linear Combination of",r"Rows","of",r"A")
+        change3.move_to(2*DOWN)
+        change3[1].set_color(DARK_BLUE)
+        change3[3].set_color(DARK_BLUE)
+
+        self.play(Write(change1))
+        self.play(Write(change2))
+        self.play(Write(change3))
+
+        columns = TextMobject("Columns")
+        columns.scale(0.6)
+        columns.set_color(DARK_BLUE)
+        columns.move_to(2*DOWN+4.1*RIGHT)
+
+        a = TextMobject(r"$A^{T}$")
+        a.set_color(DARK_BLUE)
+        a.move_to(1.95*DOWN+5.6*RIGHT)
+
+        self.wait(0.5)
+
+        self.play(Transform(change3[1],columns), Transform(change3[3],a))
+
+        equal = TextMobject(r"= Column Space($A^{T}$)")
+        equal.move_to(3*DOWN+0.5*RIGHT)
+
+        self.play(Write(equal))
+
+        self.play(FadeOut(A_T), FadeOut(change1), FadeOut(change2), FadeOut(change3), FadeOut(A), FadeOut(equal))
+
+        ac_defn1.move_to(3*UP)
+        RS_A.move_to(1.5*UP)
+        RS_A[6].move_to(UP)
+        RS_A[7].move_to(UP+1.5*RIGHT)
+        
+        self.play(Write(RS_A),FadeIn(ac_defn1))
+        
+        CS_AT = TextMobject(r"Row Space of $A = x_{1}$",
+        r"$\left( \begin{array}{c} 1 \\ 2 \\ 1 \end{array} \right)$",
+        r"$+x_{2}$",
+        r"$ \left( \begin{array}{c} 1 \\ 3 \\ 1 \end{array} \right)$",
+        r"$ + x_{3}$",
+        r"$\left( \begin{array}{c} 2 \\ 1 \\ 4 \end{array} \right)$",
+        r"$+x_{4}$",
+        r"$ \left( \begin{array}{c} 3 \\ 2 \\ 3 \end{array} \right)$")
+        CS_AT.move_to(1.5*DOWN)
+        CS_AT[1].set_color(color = DARK_BLUE)
+        CS_AT[3].set_color(color = DARK_BLUE)
+        CS_AT[5].set_color(color = DARK_BLUE)
+        CS_AT[7].set_color(color = DARK_BLUE)
+        CS_AT.scale(0.75)
+        
+        ac_defn2 = TextMobject("According to Definition 2 : ")
+        equivalent = TextMobject(r"Hence, Definition 1 $\equiv$ Definition 2")
+        equivalent.move_to(3*DOWN)
+
+        self.play(Write(CS_AT),FadeIn(ac_defn2))
+        self.play(Write(equivalent))
+
+        self.wait()
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
new file mode 100644
index 0000000..5c48a13
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
@@ -0,0 +1,3 @@
+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
new file mode 100755
index 0000000..e54276c
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
@@ -0,0 +1,97 @@
+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