Linear Algebra: Linear Systems and Matrix Algebra (full lecture)

We introduce the rank of a matrix and matrix algebra including the product of a matrix and a vector.

[sechokito]

you cant imagine how I am thankful to you. Thank you

[biggo]

Dear Dr. Hower, thank you for your motivating (always smiling) lectures. As I am refreshing my Linear Algebra. Thank you again for going an extra mile.

[louiscorprew]

I’m really enjoying these lectures. Thank you for all the time and effort you put into these!

[tmann]

Passed my calculus 2 last semester! Thank you for all the help! Now I’m taking linear algebra this summer 😄

[jan-willemreens]

Good day Dr.Valerie, Just finished another of your now world famous lectures on Linear Algebra if I also may believe the other positive comments. I would like to add something to your clear presentation if you do not object. You can also distinguish the three possible solutions of a system of linear equations as follows: 1) A system with one unique solution is called consistent and independent...2) A system with infinitely many solutions is called consistent and dependent...3) A system without solution(s) is called inconsistent. Of course I'm fully convinced that you already know this, I just thought maybe naming the terms 'dependent and independent' could be a small but not unimportant addition. So nice to see that such a system can be interpreted in several ways and of which I like the way of a linear combination of the column vectors of a given matrix; fascinating! This was new to me, and it feels more intuitive than the dot product way. By the way Dr. Valerie, I can see that you need to have quite a bit of dancing skills to be able to explain the dot product of vectors; to be honest I'm not a good dancer myself! Dr. Valerie, happy Valentine's Day to the most entertaining teacher on the internet!

[sonaraghavan]

Concepts have been presented in a crystal clear manner. Amazing!

[marvelousncube]

I am self studying linear algebra through the internet. As a person who is studying to know linear algebra it's self not to get a certain degree or some special document, this have been helpful to me honestly it boosted my studying spirit, Thank you so much❤❤

[maxpercer]

1:00:38 I like how you displayed 3 rref moves and lined them up next to the rows they will replace. Very neat.

[maxpercer]

Great video. My book uses A_mxn for the dimensions of the coefficient matrix, so i will use that instead of n x m. I wish they standardized these things.

[scottgreen]

All those antic over some chalk and a chalk board. Yea I’m learning something. I’m sixty five so it will never mean much despite my computer science and electronics degree. Fifteen minutes a day then I’m going to go over the Krebs and Calvin cycles of biology chemistry wise. That’s why this is so much fun.

[DetlefHess]

Dr. Hower, one thing I am curious about is why texts even mention row echelon form? Why not only talk about *reduced* REF? Maybe I missed this somewhere in your lecture? It seems to me that one would always want to go fully to RREF (assuming the system is consistent of course). What is the value of only REF? Fantastic series. Thank you!

[freizagen]

In previous video at 42:05 you said the vector will be a line. How did you know whether it is a point, line, plane or entire Rn

[peterloulee]

Nokia rejected the android program, why