From e00ca1cc61a2bac650456df7d93ca1dcfd72838c Mon Sep 17 00:00:00 2001 From: simranchhattani Date: Sun, 19 Jul 2020 22:43:12 +0530 Subject: Add files via upload --- .../MCQ/Basis of a Vector Space and its Subspace.docx | Bin 0 -> 13069 bytes .../MCQ/Dual of a Space MCQ Questions.docx | Bin 0 -> 13525 bytes .../MCQ/Inner Product Space MCQ Questions.docx | Bin 0 -> 13559 bytes .../Polynomial and Function Spaces MCQ Questions.docx | Bin 0 -> 13345 bytes .../Vector-Spaces/MCQ/Vector Spaces MCQ Questions.docx | Bin 0 -> 14568 bytes 5 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Basis of a Vector Space and its Subspace.docx create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Dual of a Space MCQ Questions.docx create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Inner Product Space MCQ Questions.docx create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Polynomial and Function Spaces MCQ Questions.docx create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Vector Spaces MCQ Questions.docx (limited to 'FSF-2020') diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Basis of a Vector Space and its Subspace.docx b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Basis of a Vector Space and its Subspace.docx new file mode 100644 index 0000000..0dbfc4f Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Basis of a Vector Space and its Subspace.docx differ diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Dual of a Space MCQ Questions.docx b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Dual of a Space MCQ Questions.docx new file mode 100644 index 0000000..1731a8f Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Dual of a Space MCQ Questions.docx differ diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Inner Product Space MCQ Questions.docx b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Inner Product Space MCQ Questions.docx new file mode 100644 index 0000000..80ee81c Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Inner Product Space MCQ Questions.docx differ diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Polynomial and Function Spaces MCQ Questions.docx b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Polynomial and Function Spaces MCQ Questions.docx new file mode 100644 index 0000000..7904fd1 Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Polynomial and Function Spaces MCQ Questions.docx differ diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Vector Spaces MCQ Questions.docx b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Vector Spaces MCQ Questions.docx new file mode 100644 index 0000000..338b6f3 Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/MCQ/Vector Spaces MCQ Questions.docx differ -- cgit From 5253ed473b10fc271dd457ea7d80d8e8dc7f1702 Mon Sep 17 00:00:00 2001 From: simranchhattani Date: Mon, 20 Jul 2020 01:06:57 +0530 Subject: Add files via upload --- .../linear_dependence_and_independence.py | 293 +++++++++++++++++++++ 1 file changed, 293 insertions(+) create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/linear_dependence_and_independence.py (limited to 'FSF-2020') diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/linear_dependence_and_independence.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/linear_dependence_and_independence.py new file mode 100644 index 0000000..b092777 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/linear_dependence_and_independence.py @@ -0,0 +1,293 @@ +from manimlib.imports import * +class Linear_Dependence(ThreeDScene): + + def construct(self): + + axes = ThreeDAxes() + axes.set_stroke(width=1,color=GOLD) + self.add(axes) + self.set_camera_orientation(phi = 70*DEGREES,theta =110*DEGREES) + self.begin_ambient_camera_rotation(rate=0.05) + self.wait(0.5) + text1 = TextMobject(r"Consider 3 linearly dependent vectors in $\mathbb{R}^3$").scale(0.5).shift(2.5*UP+4*LEFT) + line1 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [-1,1,1]) + self.add_fixed_in_frame_mobjects(text1) + self.play(ShowCreation(text1)) + self.play(ShowCreation(line1)) + self.wait(1) + line2 = Line(color = RED,opacity=350,start = ORIGIN,end = [1,0.5,0.5]) + self.play(ShowCreation(line2)) + self.wait(1) + line3 = Line(color = BLUE,opacity=350,start = ORIGIN,end = [0.5,1,1]) + self.play(ShowCreation(line3)) + self.wait(1) + text2 = TextMobject("Scaling the Vectors").scale(0.5).shift(2.5*UP+4.5*LEFT) + text3 = TextMobject(r"\text{and}",r"\text{Adding}",r"\text{them}").scale(0.5).shift(2*UP+4.5*LEFT) + text3[1].set_color(GREEN) + + + line4 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [-2,2,2]) + line5 = Line(color = RED,opacity = 350,start = ORIGIN,end = [3,1.5,1.5]) + line6 = Line(color = BLUE,opacity = 350,start = ORIGIN,end = [-0.5,-1,-1]) + self.wait(1.1) + self.play(FadeOut(text1)) + self.add_fixed_in_frame_mobjects(text2) + self.play(ShowCreation(text2)) + self.wait(0.7) + self.play(Transform(line1,line4)) + self.wait(0.5) + self.play(Transform(line2,line5)) + self.wait(0.5) + self.play(Transform(line3,line6)) + + self.wait(1.5) + + line7 = Line(color = RED,opacity = 350,start = [-2,2,2],end = [1,3.5,3.5]) + line8 = Line(color = BLUE,opacity = 350,start = [1,3.5,3.5],end = [0.5,2.5,2.5]) + line9 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [0.5,2.5,2.5]) + + self.add_fixed_in_frame_mobjects(text3) + self.play(ShowCreation(text3)) + self.wait(0.7) + self.play(FadeOut(line2),ShowCreation(line7)) + self.play(FadeOut(line3),ShowCreation(line8)) + self.wait(0.7) + self.play(ShowCreation(line9)) + self.wait(1.2) + + + plane = Polygon([-4,4,4],[4,4,4],[4,-4,-4],[-4,-4,-4]) + plane.set_opacity(0.4) + plane.set_fill(DARK_BLUE) + plane.set_color(DARK_BLUE) + self.play(ShowCreation(plane)) + self.wait(1.2) + text4 = TextMobject("Linearly Combinations").scale(0.65).shift(3.5*UP+4*RIGHT) + + text5 = TextMobject(r"\text{$\vec{z_1}$}",r"\text{=}",r"\text{2}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{3}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{(-1)}",r"\text{$\vec{w}$}",).scale(0.55).shift(2.5*UP+3.9*RIGHT) + text5[0].set_color(GREEN) + text5[3].set_color(YELLOW) + text5[6].set_color(RED) + text5[9].set_color(BLUE) + self.add_fixed_in_frame_mobjects(text5) + self.add_fixed_in_frame_mobjects(text4) + self.play(ShowCreation(text4),ShowCreation(text5)) + self.wait(3.8) + bunch1 = VGroup(line7,line8,line9) + line10 = Line(color=YELLOW,opacity=350,start=ORIGIN,end=[-0.5,0.5,0.5]) + line11 = Line(color=RED,opacity=350,start=ORIGIN,end=[2,1,1]) + line12 = Line(color = BLUE,opacity = 350,start = ORIGIN,end = [-1.5,-3,-3]) + line13 = Line(color = RED,opacity = 350,start = [-0.5,0.5,0.5],end = [1.5,1.5,1.5]) + line14 = Line(color = BLUE,opacity = 350,start = [1.5,1.5,1.5],end = [0,-1.5,-1.5]) + line15 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [0,-1.5,-1.5]) + bunch2 = VGroup(line13,line14,line15,line10) + self.play(FadeOut(line1),Transform(bunch1,bunch2)) + self.wait(1.2) + text6 = TextMobject(r"\text{$\vec{z_2}$}",r"\text{=}",r"\text{0.5}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{2}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{(-3)}",r"\text{$\vec{w}$}",).scale(0.55).shift(2*UP+4*RIGHT) + text6[0].set_color(GREEN) + text6[3].set_color(YELLOW) + text6[6].set_color(RED) + text6[9].set_color(BLUE) + + self.add_fixed_in_frame_mobjects(text6) + self.play(ShowCreation(text6)) + self.wait(2.8) + bunch3 = VGroup(line10,bunch1) + + line16 = Line(color=YELLOW,opacity=350,start=ORIGIN,end=[-2,2,2]) + line17 = Line(color=RED,opacity=350,start=ORIGIN,end=[1,0.5,0.5]) + + line18 = Line(color = RED,opacity = 350,start = [-2,2,2],end = [-1,2.5,2.5]) + + line19 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [-1,2.5,2.5]) + bunch4 = VGroup(line16,line18,line19) + self.play(Transform(bunch3,bunch4)) + self.wait(1.2) + text7 = TextMobject(r"\text{$\vec{z_3}$}",r"\text{=}",r"\text{(-2)}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{2}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{(0)}",r"\text{$\vec{w}$}",).scale(0.55).shift(1.5*UP+4*RIGHT) + text7[0].set_color(GREEN) + text7[3].set_color(YELLOW) + text7[6].set_color(RED) + text7[9].set_color(BLUE) + self.add_fixed_in_frame_mobjects(text7) + self.play(ShowCreation(text7)) + + self.wait(5) + self.play(FadeOut(text2),FadeOut(text3)) + text8 = TextMobject(r"\text{$\vec{z}$}",r"\text{=}",r"\text{a}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{b}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{c}",r"\text{$\vec{w}$}",).scale(0.55).shift(0.8*UP+4*RIGHT) + text8[0].set_color(GREEN) + text8[3].set_color(YELLOW) + text8[6].set_color(RED) + text8[9].set_color(BLUE) + rect1 = Rectangle(height=0.7,stroke_width=1.2) + rect1.surround(text8) + self.add_fixed_in_frame_mobjects(rect1) + self.add_fixed_in_frame_mobjects(text8) + self.play(ShowCreation(text8)) + text9 = TextMobject(r"\text{All the}",r"\text{linear combinations}",r"\text{of linearly dependent vectors}",r"\text{$\vec{u},$}",r"\text{$\vec{v},$}",r"\text{and}",r"\text{$\vec{w}$}",r"\text{spans}").scale(0.5).shift(2.5*DOWN) + text9[1].set_color(GREEN) + text9[3].set_color(YELLOW) + text9[4].set_color(RED) + text9[6].set_color(BLUE) + text9.add_background_rectangle() + text10 = TextMobject(r"this entire plane (and not the entire $\mathbb{R}^3 )$.").scale(0.5).shift(3*DOWN) + text10.add_background_rectangle() + self.wait(2) + self.add_fixed_in_frame_mobjects(text10) + + self.add_fixed_in_frame_mobjects(text9) + self.play(ShowCreation(text9),ShowCreation(text10)) + self.wait(7) + +class Linear_Independence(ThreeDScene): + + def construct(self): + + axes = ThreeDAxes() + axes.set_stroke(width=1,color=GOLD) + self.add(axes) + self.set_camera_orientation(phi = 70*DEGREES,theta =110*DEGREES) + self.begin_ambient_camera_rotation(rate=0.1) + self.wait(0.5) + text1 = TextMobject(r"Consider 3 linearly independent vectors in $\mathbb{R}^3$").scale(0.5).shift(2.5*UP+4*LEFT) + self.add_fixed_in_frame_mobjects(text1) + self.play(ShowCreation(text1)) + line1 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [-1,1,1]) + self.play(ShowCreation(line1)) + self.wait(0.7) + line2 = Line(color = RED,opacity=350,start = ORIGIN,end = [1,0.5,0.5]) + self.play(ShowCreation(line2)) + self.wait(0.7) + line3 = Line(color = BLUE,opacity=350,start = ORIGIN,end = [0,-1,-2]) + self.play(ShowCreation(line3)) + self.wait(0.7) + + self.wait(1) + self.play(FadeOut(text1)) + text2 = TextMobject("Scaling the Vectors").scale(0.5).shift(2.5*UP+5*LEFT) + self.add_fixed_in_frame_mobjects(text2) + self.play(ShowCreation(text2)) + self.wait(0.7) + line4 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [-0.5,0.5,0.5]) + self.play(Transform(line1,line4)) + self.wait(0.7) + line5 = Line(color = RED,opacity=350,start = ORIGIN,end = [2,1,1]) + self.play(Transform(line2,line5)) + self.wait(0.7) + line6 = Line(color = BLUE,opacity=350,start = ORIGIN,end = [0,-1.5,-3]) + self.play(Transform(line3,line6)) + self.wait(1.7) + text3 = TextMobject(r"\text{and}",r"\text{Adding}",r"\text{them}").scale(0.5).shift(2*UP+5*LEFT) + text3[1].set_color(GREEN) + + line7 = Line(color = RED,opacity = 350,start = [-0.5,0.5,0.5],end = [1.5,1.5,1.5]) + line8 = Line(color = BLUE,opacity = 350,start = [1.5,1.5,1.5],end = [1.5,0,-1.5]) + line9 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [1.5,0,-1.5]) + self.add_fixed_in_frame_mobjects(text3) + self.play(ShowCreation(text3)) + self.wait(0.7) + self.play(FadeOut(line2),ShowCreation(line7)) + self.play(FadeOut(line3),ShowCreation(line8)) + self.wait(0.7) + self.play(ShowCreation(line9)) + self.wait(1.5) + plane = Polygon([-4,4,4],[4,4,4],[4,-4,-4],[-4,-4,-4]) + plane.set_opacity(0.3) + plane.set_fill(DARK_BLUE) + plane.set_color(DARK_BLUE) + self.play(ShowCreation(plane)) + self.wait(1.2) + text4 = TextMobject("Linearly Combinations").scale(0.65).shift(3.5*UP+4*RIGHT) + self.add_fixed_in_frame_mobjects(text4) + self.play(ShowCreation(text4)) + self.wait(0.7) + text5 = TextMobject(r"\text{$\vec{z_1}$}",r"\text{=}",r"\text{0.5}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{2}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{1.5}",r"\text{$\vec{w}$}").scale(0.55).shift(2.5*UP+3.8*RIGHT) + text5[0].set_color(GREEN) + text5[3].set_color(YELLOW) + text5[6].set_color(RED) + text5[9].set_color(BLUE) + self.add_fixed_in_frame_mobjects(text5) + + self.play(ShowCreation(text5)) + self.wait(3.8) + bunch1 = VGroup(line7,line8,line9) + line10 = Line(color=YELLOW,opacity=350,start=ORIGIN,end=[-3,3,3]) + + line11 = Line(color = BLUE,opacity = 350,start = [-3,3,3],end = [-2,3.5,3.5]) + + + line12 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [-2,3.5,3.5]) + bunch2 = VGroup(line10,line11,line12) + self.play(FadeOut(line1),Transform(bunch1,bunch2)) + self.wait(1.2) + + text6 = TextMobject(r"\text{$\vec{z_2}$}",r"\text{=}",r"\text{3}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{1}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{0}",r"\text{$\vec{w}$}").scale(0.55).shift(2*UP+3.6*RIGHT) + text6[0].set_color(GREEN) + text6[3].set_color(YELLOW) + text6[6].set_color(RED) + text6[9].set_color(BLUE) + + self.add_fixed_in_frame_mobjects(text6) + self.play(ShowCreation(text6)) + self.wait(2.8) + bunch3 = VGroup(line10,bunch1) + + line13 = Line(color=YELLOW,opacity=350,start=ORIGIN,end=[2.5,-2.5,-2.5]) + line14 = Line(color=RED,opacity=350,start=[2.5,-2.5,-2.5],end=[0.5,-3.5,-3.5]) + + line15 = Line(color = BLUE,opacity = 350,start = [0.5,-3.5,-3.5],end = [0.5,-0.5,2.5]) + + line16 = Line(color = GREEN,opacity = 350,start = ORIGIN,end = [0.5,-0.5,2.5]) + bunch4 = VGroup(line13,line14,line15,line16) + self.play(Transform(bunch3,bunch4)) + self.wait(1.2) + text7 = TextMobject(r"\text{$\vec{z_3}$}",r"\text{=}",r"\text{(-2.5)}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{(-2)}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{(-3)}",r"\text{$\vec{w}$}").scale(0.55).shift(1.5*UP+4.2*RIGHT) + text7[0].set_color(GREEN) + text7[3].set_color(YELLOW) + text7[6].set_color(RED) + text7[9].set_color(BLUE) + self.add_fixed_in_frame_mobjects(text7) + self.play(ShowCreation(text7)) + self.play(FadeOut(text3),FadeOut(text2)) + self.wait(1.2) + text8 = TextMobject(r"\text{$\vec{z}$}",r"\text{=}",r"\text{a}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{b}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{c}",r"\text{$\vec{w}$}").scale(0.55).shift(0.8*UP+3.6*RIGHT) + text8[0].set_color(GREEN) + text8[3].set_color(YELLOW) + text8[6].set_color(RED) + text8[9].set_color(BLUE) + rect1 = Rectangle(height=0.7,stroke_width=1.2) + rect1.surround(text8) + self.add_fixed_in_frame_mobjects(rect1) + self.add_fixed_in_frame_mobjects(text8) + self.play(ShowCreation(text8)) + self.wait(1.7) + self.play(FadeOut(plane)) + self.wait(1.5) + text9 = TextMobject(r"\text{All the}",r"\text{linear combinations}",r"\text{of linearly independent vectors}",r"\text{$\vec{u},$}",r"\text{$\vec{v},$}",r"\text{and}",r"\text{$\vec{w}$}",r"\text{spans}").scale(0.5).shift(2.5*DOWN) + text9[1].set_color(GREEN) + text9[3].set_color(YELLOW) + text9[4].set_color(RED) + text9[6].set_color(BLUE) + text9.add_background_rectangle() + text10 = TextMobject("not only the plane but the entire 3-D space.").scale(0.5).shift(3*DOWN) + text10.add_background_rectangle() + self.add_fixed_in_frame_mobjects(text9) + + self.add_fixed_in_frame_mobjects(text10) + self.play(ShowCreation(text9),ShowCreation(text10)) + self.wait(2.3) + + self.play(FadeOut(text5),FadeOut(text6),FadeOut(text7)) + self.wait(0.6) + text9 = TextMobject(r"\text{$\vec{z}$}",r"\text{=}",r"\text{a}",r"\text{$\vec{u}$}",r"\text{+}",r"\text{b}",r"\text{$\vec{v}$}",r"\text{+}",r"\text{c}",r"\text{$\vec{w}$}",r"\text{= 0}").scale(0.55).shift(2.6*UP+3.9*RIGHT) + text9[0].set_color(GREEN) + text9[3].set_color(YELLOW) + text9[6].set_color(RED) + text9[9].set_color(BLUE) + text10 = TextMobject("only when a = b = c = 0.").scale(0.55).shift(2.2*UP+3.9*RIGHT) + self.play(FadeOut(text8),FadeOut(rect1)) + self.wait(0.7) + self.add_fixed_in_frame_mobjects(text9) + self.add_fixed_in_frame_mobjects(text10) + + self.play(ShowCreation(text9),ShowCreation(text10)) + self.wait(5) -- cgit From a84df28284d3ce9c1230a9f1165ae1f095483648 Mon Sep 17 00:00:00 2001 From: simranchhattani Date: Mon, 20 Jul 2020 01:12:57 +0530 Subject: Add files via upload --- .../gifs/Linear-Dependence-and-Independence.mp4 | Bin 0 -> 12080022 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear-Dependence-and-Independence.mp4 (limited to 'FSF-2020') diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear-Dependence-and-Independence.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear-Dependence-and-Independence.mp4 new file mode 100644 index 0000000..c44801f Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear-Dependence-and-Independence.mp4 differ -- cgit From ada40f02cac6feeec2cdc6ef66fc867136f0ba44 Mon Sep 17 00:00:00 2001 From: simranchhattani Date: Mon, 20 Jul 2020 02:16:30 +0530 Subject: Add files via upload --- .../gifs/Basis_generating_the_whole_2D_space.mp4 | Bin 0 -> 10252339 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_generating_the_whole_2D_space.mp4 (limited to 'FSF-2020') diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_generating_the_whole_2D_space.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_generating_the_whole_2D_space.mp4 new file mode 100644 index 0000000..9a43846 Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_generating_the_whole_2D_space.mp4 differ -- cgit From a8055434b88686ffd9956da9551be1cdc251ec4e Mon Sep 17 00:00:00 2001 From: simranchhattani Date: Mon, 20 Jul 2020 02:18:50 +0530 Subject: Delete Basis_of_a_Subspace.mp4 --- .../Subspaces/gifs/Basis_of_a_Subspace.mp4 | Bin 10735096 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 (limited to 'FSF-2020') diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 deleted file mode 100644 index d384f80..0000000 Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 and /dev/null differ -- cgit