Parametric representations of lines | Vectors and spaces | Linear Algebra | Khan Academy

Parametric Representations of Lines in R2 and R3

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

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[AntoineSarhan]

Sal, I want to personally thank you for everything you are doing. You left a lucrative hedge fund job to teach the world and you have helped me and so many others with your videos. You are better than all my math professors I've ever had combined and you really help. Going to the core of the problem rather than me memorizing each step to get an answer. First paycheck I get after university I'm donating all of it to Khan Academy!

[БидонКадыкавич-хц]

"Linear algebra is just a more painful way of doing what you already knew how to do"
- best teacher ever

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Would someone please give this guy a medal already .
Thank you.

[HunteronX]

Thank you very much for this. It has and will be very useful in the test I have coming up.

I think that the main difference between your method of teaching and other methods that I have experienced, is that you don't take any shortcuts (at least to my knowledge), so things are not misunderstood.

[flytrapYTP]

I feel like I now understand the purpose of this line representation, thank you.

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Khan Academy is my life-saver! Very educational videos and he makes the math actually easy instead of messing around like many of my teachers/lecturers do. Great job! :)

[MrTrainWrreck]

Whats amazing about his teaching is that I have visuals. The biggest problem with my teacher is that he does not show the class visuals and I can't learn.

[emailpreet]

Thanks for the videos on Linear Algebra

[knife_wizard]

Your kind-of unfocused explanation of parametric equations(understandable, because the video's not about parametric equations) made more sense to me than any math book where I've read ahead to try and teach myself parametrics, because my teachers all refused to teach it, even when I've asked. I'm going into college this year, so I kind of have to watch your linear algebra series. Good thing it's so awesome ;)

[Iverass]

I wish these were available when I studied at univeristy!

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I really appreciate your doing this. My teacher tries, but he really is inapt at teaching this subject (or at least with teaching methods he uses). This, however, works like a charm. It turns what seems like a foriegn language to more of an adcanced english.

[lihaozheng]

Really awesome video, makes a lot sense to me ! Thanks !

[cindyo]

Hmm, I actually loved the video. I took linear algebra in college and this was a great refresher. I actually understand it more now than I did then.

[Chris-oujx]

This is amazing, it's really instrumental for a senior high to comprehend these core concepts! Thank you so much!

[lakshmin]

This video specifically on the parametric representation of line was very interesting....

[JThorssN]

Awesome! I was having a lot of trouble with this earlier today, but now it's the easiest thing in the world. Thanks a lot!!

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Im not new to youtube but I still dont know;
Which youtube-clip comes after this one in order, and how do I pick the right one because THIS STUFF IS AMAZING I NEED TO WATCH MORE! :)

[jbone]

hey man, i just want to say thank you. posting up such helpful knowledge with the only benefit being teaching others is truly a great thing. you have significantly increased my understanding of all this material and i feel extremely confident for my finals. its upsetting that students pay institutions thousands of dollars for instruction worse than reading a book when there are true educators like yourself. thanks so much

[mintoocool]

how does one mentally imagine something beyond 3 dimensions ? if i can visualize that i m set for life!

[krishnamusalimadugu]

Hey I enjoyed this content a lot it doesn't felt me bored but I endup with a doubt in the end what if the points given for me are three and not two then still can I apply this with taking any two out of three given points?