What's the big idea of Linear Algebra? **Course Intro**

This is the start of a one semester university level course on Linear Algebra that emphasizes both conceptual understanding as well as procedural fluency with the techniques of Linear Algebra. In this video, we get to see just the beginning of some of the big ideas of Linear Algebra.

Linear Algebra is a story told in two worlds, one geometric and one algebraic. The interplay between the two is beautiful and powerful. In this video we introduce the notion of a linear transformation and see how this simplification makes our lives far easier.

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Linear Algebra course taught by Dr. Trefor Bazett

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[gastondupertuis]

First of all sorry if my English isn't perfect. I'm from Argentina.
I'm near 42 years old and started this year to study Electronic Engineering. Is never to late :)
This is my first comment ever in a YouTube video and I want to encourage you to keep posting more videos because they are very good.
Great explanations.
I hope more people could discover your channel.
Thank you very much and keep going!

[ryantierney]

Currently taking linear algebra at Harvard and studying for my midterm, your explanations are coming in clutch.

[michellechal]

you have NO IDEA HOW HELPFUL YOUR VIDEOS ARE <3

[ZeerobForever]

I have been taught linear algebra at school a long time ago. Matrix operations, multiplying matrices, etc. But is was never really clear to me what these numbers actually meant. I saw your 13 minute video, and now it is finally clear to me what a matrix actually stands for. Thanks a lot!

[ModiSaurabhMehulBEE]

For those who are not able to feel linear algebra even after studying it somewhere(in college or by some book), do one thing just binge-watch videos up to 50 videos consecutively. It would take about 4-6 hours and then you will know what is the motivation behind the different concepts. I did it and one takeaway that I drew is that linear algebra is a study to develop types of algorithm to visualize the vectors and systems of linear equations. It's very useful to develop useful computational algorithms as it makes the job more modular and recursive for computers to apprehend. It might sound vague but think of it after watching videos and you will get ideas of making several algorithms to solve problems like making a program to find the solution to a system of equations, making a program to find the rotational coordinates in a system, etc.

[MrMentholSlim]

30 year old burn out going back to school. your videos are impossibly helpful for understanding stuff in a "less formal" way then taught in class.

[WhySoSerious]

People like you are what makes the internet such a blessing.

[ninaddongare]

All my school I thought math is such a waste of time with no use.
I wish I had a teacher this passionate, I probably had a different career at this time.
Anyway, better late than never.

[GautamKhatter]

This is the video that solved the confusion in my mind about linear algebra that has been stuck in my brain for days now.
Thank you for explaining this with such easy examples.
Would love to see something like this for the higher dimensions.

[nicholaschan]

You’re a fantastic teacher.. I wish I found this video sooner! Cheers sir 🙏

[skipintro]

I studied linear algebra at university; but actually learned from this playlist. Unarguably it is the best place to learn linear algebra on the internet. I wish he was my math teacher at high school.

[SaimKhan-xjum]

you are awesome, please dont stop posting

[Ianwong]

Professor Bazett, I was one of your students in MAT223 (The Linear Algebra course) when u were still in UofT. I did not expect I would see you again on youtube. Thanks for your teaching anyway! Keep up the good work

[michelledlr]

im gonna study engeniering chemistry and i think i got pretty clear the idea of what linear algebra is

[FirstLast-gklg]

Awesome! Never got past Algebra 2 in high school and about to start Computer Science next week lol so I am binging Linear Algebra stuff and this content is exactly what I was looking for! About to binge watch that playlist you had at the end of the video, thank you.

[pkhnuzk]

your explanation of how a matrix relates to individual vectors with the graphics was great

[AbuSayed-ervs]

Mind blowing!!!Your linear algebra videos are really really good to understand to get a clear picture.

[pjakobsen]

Outstanding intuition -really excited about this course. Thank you Trefor!

[daisyg]

My god. I'm in linear right now and having trouble understanding why we're doing this math but in a matter of minutes it makes more sense to me. Thank you.

[picklerick]

At 11:55, the inverse matrix should have been:
[1/3 1/3
-1/3 2/3]