Matrix vector products | Vectors and spaces | Linear Algebra | Khan Academy

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Defining and understanding what it means to take the product of a matrix and a vector

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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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I was looking for a Turkish video but I never found a nice and clear one so I found this video. This video really helped my finals Thanks!

ezgi
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These are all the basics of what you need for the more advanced courses. They are like introductions for continued studies.

Syeal
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I think at 1:03, it should be am1 not amn

mengs
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I'm taking differential equations two years after taking linear algebra, this is a great refresher. Thanks!!

audreym
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Just noting that bn at 8:16 should be bm.

clarencehung
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KHHAAAANNN!!!
You're gonna have to be less abstract Khan.
You're gonna have to come down here to our level Khan!

archentity
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not what i was looking for but still great video! =]

purenight
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Thanks, this helped me on my assignment.

Jackyxz
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14:16 This should be a1(Transposed).X and a2(Transposed).X because you can't dot product a column vector with a column vector right?

HarshvardhanKanthode
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Gracias por la explicación desde colombia me permitiste ver diferentes puntos de vista para aplicar la multiplacion de un escalar por una Matriz

valeriagullo
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I live in Belgium and about everything in these vids is what I either saw in secondary school or first semester of university (phisics and astrology).

Wouterdobbels
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at 19:35 why the product Ax can be interpreted as a linear combination depending of the x vector?, depending on the number of rows or columns or maybe if the components are not linear like x but cuadratic like x^2?

smc
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Why there is a need to convert the matrix as vectors and that to by dividing the matrix as column vectors , Pls anyone can Answer my doubt over here.

jaiganeshbaskar
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Great teacher..clear voice and pronunciation..clear instructions

rasikajayathilaka
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The last part doesn't make sense as Ax(x is vector..I cannot write it here) has to have (4x1) component not a number. To make it a sense, it should be told like the sum of whole component of Ax(not just Ax) is linear combination of row vectors of A. I came here on youtube from Kahn academy to raise this question.

ekdkseho
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Dat mistake. I caught it... But that warrants a correction!

satisfiction
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At the end of this course, what level of Linear Algebra will I have (assuming I master all video topics)?

DelphianSociety
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Man I can not find a video that explains how to do it using the "sum" notation

DisIoss
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You said a matrix is a 2 dimensional array. Is an n dimensional array a tensor then? Honestly I've never known what a tensor was.

LernRead
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@12:38 a1 vector has 4 component !!! is that 4th dimension ?

emu