[Linear Algebra] Subspace Proof Examples

We show that if H and K are subspaces of V, the H intersection K is a subspace of V.

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#LinearAlgebra #Algebra #UniversityMath #Lecture

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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[juanlemod]

This is the video where I discovered you. I wish I discovered your channel weeks ago. Now I feel hope that I can be successful in my upper-division Linear Algebra course. I’m subscribed.

The examples in this video opened my eyes to stuff I was not seeing. I wasn’t sure how to present the stuff I was trying to prove. Everything clicked. I’m extremely grateful for your videos.

I understand this video is years old, but it would be helpful if, at the end of each example you gave, you would write a formal proof incorporating all the stuff you just shown.

I have been struggling in my upper-division Linear Algebra course and writing proofs. Even though I earned an A in my lower-division Linear Algebra course and learnt a lot in my Discrete Math course where they taught me how to write proofs and different proof techniques, I’ve been having a difficult time applying what I learnt in my Discrete Math course to my upper-division Linear Algebra course, especially when it comes to deconstructing what I’m trying to prove into logical statements in order to mechanically transform the logically statements into other equivalent logical statements into progressing charts of Givens and Goals.

I like making these Given and Goal charts and using them as scratch work before writing the actual formal proof. In this upper-division Linear Algebra course, I haven’t been able to do that.

[muhammed_ajwad]

I wish I knew you months ago. You are awesome man. Thank you.
Keep going. Love you.

[digitalfroot]

these are cute little proofs lol they’re so perfect

[yueleichen]

i now feel like i have a chance for a high grade in my linear course

[joshuabloodymierpolicarpio]

wouldn't be much easier for the second proof to manipulate the actual given cu=0 where u=0 for non-zero c, instead of doing it by manipulating with the other axiom.

[XSilverX]

2nd is so weird, I'm just like why.