From 9c93f9fd57d3d12355e5fb854603e421965a08c1 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Tue, 7 Jul 2020 18:47:41 +0530
Subject: semi-final 4FSS

---
 .../file3_solution.py                              | 77 ++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py

(limited to 'FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py')

diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py
new file mode 100644
index 0000000..eb310f3
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py
@@ -0,0 +1,77 @@
+from manimlib.imports import *
+class solution(LinearTransformationScene):
+    def construct(self):
+
+        self.setup()
+        self.wait()
+        
+        o = TextMobject(r"This is the original vector space $R^2$ (before Linear Transformation)")
+        o.move_to(3*DOWN)
+        o.scale(0.75)
+        o.add_background_rectangle()
+        self.play(Write(o))
+        self.wait()
+        self.play(FadeOut(o))
+
+        A = TextMobject(r"Consider the matrix the of this linear transformation $A$ = $\left[\begin{array}{c c} 1 & -1 \\  1 & -1 \end{array}\right]$")
+        A.move_to(3*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")
+        o.move_to(3*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(PURPLE)
+        arrow2.scale(1.2)
+        self.play(ShowCreation(arrow2))
+        self.wait()
+
+        o1 = TextMobject("If the ","vector b"," lies in the transformed vector space")
+        o2 = TextMobject("(the line) then the solution exist")
+        o1.move_to(2.5*DOWN+2*RIGHT)
+        o1[1].set_color(PURPLE)
+        o2.move_to(3*DOWN+2.5*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(ORANGE)
+        arrow1.scale(1.3)
+        self.play(ShowCreation(arrow1))
+        self.wait()
+
+        o1 = TextMobject("If the ","vector b"," does lies in the transformed")
+        o2 = TextMobject("vector space then the does not solution exist")
+        o1.move_to(2.5*DOWN+2*RIGHT)
+        o1[1].set_color(ORANGE)
+        o2.move_to(3*DOWN+2.5*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
-- 
cgit