Rowspace and left nullspace | Matrix transformations | Linear Algebra | Khan Academy
ฝัง
- เผยแพร่เมื่อ 27 ส.ค. 2024
- Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Rowspace and Left Nullspace
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
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
Subscribe to KhanAcademy’s Linear Algebra channel:: / channel
Subscribe to KhanAcademy: www.youtube.co...
Thank you for this. My professor never actually taught us this and is putting it on the exam I am taking in an hour
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!?
Much needed review, just in time. Great vid!
17:51; so that's the actual reason for the term LEFTNULLSPACE
g strang teaches a bit hazy
I wish I understand the book as much as I understand watching this video.
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.
Good job teaching..!
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.
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.
Hey I have a question. How can you find the zero vector of a basis U with respect to the standard basis E?
hm interesting question
Beautiful :)
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?
+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.
Why you always choose simple matrix which simplified only 1 row left????
U are my God..
crap dammit! why can't you be my proffesor???
why name the video rowspace and left null space ? and then go on to explain column space, and barely anything about rowsapce
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
explanation is not helpful