Rowspace and left nullspace | Matrix transformations | Linear Algebra | Khan Academy

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Rowspace and Left Nullspace
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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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[@GeorgeNavarro]

Thank you for this. My professor never actually taught us this and is putting it on the exam I am taking in an hour

[@kevinmm20]

What a great explaination! See, you understand this and were able to explain this perfectly. Now that I understand it, this stuff isn't that difficult. So why is it that some text books and teachers like to make it difficult!?

[@debendragurung3033]

17:51; so that's the actual reason for the term LEFTNULLSPACE

[@Nishchay-fk5lr]

g strang teaches a bit hazy

[@gustavovbarroso]

Much needed review, just in time. Great vid!

[@lemyul]

I wish I understand the book as much as I understand watching this video.

[@lutherhoward7637]

Because you are not concentrating when you read. Reading math and physics books takes total concentration and reading sections more than once. Then, writing the concepts in your own words. Or teach it to someone. Lincoln studied by reading out loud.

[@davidsalcido1257]

Good job teaching..!

[@HotPepperLala]

As much I as thank you for this video, you really didn't need to extend this for 23 mins, especially when the first 8 minutes is just review and you could have prepared the rref(M) ahead of time. I miss your straightforward videos in the past.

[@mky3405]

At 14:45, does Sal mean "column space of the R transpose matrix"?
if not, what is "column span"?
He sometimes says "column span", and it confused me.

[@parnashish1910]

Beautiful :)

[@Rovshenification]

Thank you for this video.
But I have a one question.
We can determine the basis by number of vectors in our Matrix, right? For ex., we have three vectors (column) in matrix, thus dimension should be 3D space, yes?

[@Postermaestro]

+Rovshen A-ev
You can determine the basis of the column space of a matrix by counting the number of pivot entries in our reduced row echelon form of the matrix. If you have 3 pivot entries in your rref-matrix, that means that you have 3 linearly independent column vectors in your matrix. Thus, the dimension of the column space of the matrix is 3, or in other terms: the rank of the matrix is 3.

[@fuahuahuatime5196]

Hey I have a question. How can you find the zero vector of a basis U with respect to the standard basis E?

[@tis_i_sana]

hm interesting question

[@sanjaykrish8719]

U are my God..

[@msaleem9704]

No

[@Philips85281]

Why you always choose simple matrix which simplified only 1 row left????

[@msaleem9704]

:(

[@ionglacier]

crap dammit! why can't you be my proffesor???

[@msaleem9704]

he can't

[@dupham7900]

why name the video rowspace and left null space ? and then go on to explain column space, and barely anything about rowsapce

[@QuickishFM]

because the rowspace is just the column space of the transposed matrix of A. You just find the column space again for the transposed matrix, which is the row space for the original non-transposed matrix

[@malharjajoo7393]

explanation is not helpful

[@msaleem9704]

whyy ?