Adding vectors | Vectors and spaces | Linear Algebra | Khan Academy

Missed the previous lesson?

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.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

[davidevans]

Thank you so f***ing much, no one answers my curiosity but your videos.

[farhajhasan]

how do u make these so easy? u r really a great TEACHER.

[jimumele]

even though I live in remote area I always have khan academy.... thank you sir. god bless you and your team

[satheeshkumar]

Thank you for the clear explanation ^^

[ashwini]

Mind Blowing Tutorial !! (I'm a Law Graduate, but suddenly got reinforced my interest in math by this video)

[NiharikaAChirayil]

Thanks for the video! It helped me out!

[disciplechoi]

Excellent explanation. Thank you so much for this.

[LaraSchilling]

I am so crying because my university class teaches vectors without matrices from the first go. Matricies are now part of the subject, but I can't handle this cartesian "remember all the values of all the coordinates" when they look like a=(x, y) or (a1, a2) or (ax, ay) etc (and it only gets worse in 3 dimensions). We only touch on matrices in cross product and using unit vectors. MATRICES ARE SO MUCH MORE CONVENIENT AND EASY TO MANIPULATE ON PAPER, yet they continue to give us annoying component based addition and subtraction like it's easier to actually keep all the values in our head and in such an unorganized manner on paper.

[arsnakehert]

Quando o instrutor fala "membros do R^2", nas legendas em português está escrito "membros do segundo quadrante." Cuidado!

When the instructor says "members of R^2", in the Portuguese subtitles it's written "members of the second quadrant." Beware!

[rushankhan]

my intuitions say that he would be pretty good at an fps. lol XD

[acespade]

oh lord! ( if u do exist ) plz bless his soul lol

[dineshchandrasoni]

But the third side of the triangle can't be equal to the sum of the other two sides...??

[shrooq_sami]

can i find this course translated in the arabic ??
please tell me

[lipton]

How r u adding them when them when they are going in different directions

[Professor_O]

I have doubt that any rule in mathematics to start a vector from the origin?

[tofailahmad]

please give me answer"a vector of magnitude 20 is added to a vector of magnitude 25. the magnitude of their sum might be?

[mathsunmasked]

Nice job. What program are you using to do these graphics?

[t.papache]

how is vector A the same when it has been plotted differently

[padmajachitta]

it would be far better if he wouldn't keep changing between colours...i know that the colours give a clear dishtinguishing detail....but it would be way smoother if he did not....no disrespect though....i love his teaching methodology

[justinchen]

*a* + *b* = *c*
a^2+b^2=c^2
sound familiar?