[Linear Algebra] Row Space and The Rank Theorem

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We introduce the concept of Row Space, Rank, and prove the Rank Theorem.'

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This was a good, clear introduction into row space and rank. Thank you!

KLCII

Hi. I took A and worked on it to make B. However, when I added R1 to R2 for a new R2, I got 0 -2 5 8. Where did the -6 come from??? When I accomplished RREF my last row was 0 0 0 1. I couldn't make a row of zeros.

kennethcramm

4:10 so basically the (vector set of A spanning the vector space) + (the vector set of A taking us to zero) = (number of columns)

CrittingOut

You are the best. I was so lost before I found your channel. Thank you so much.

cec

rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix

rolfjohansen

7:45 so would a 4x6 matrix have a minimum NulA of 2?
so Nul space is the columns that aren't a pivot and a column will be forced to be null of there are no more rows to add a pivot position to. Right?

timothygooding

What's the difference between row space and basis of row space?

tusharthakkar

Did you selected pure math for masters?

MuhammadIsmail-unqd

thanks man

next time include better tags etc in your video so it shows up in our search
i m a subscriber still i couldn't find your vids on this topic

informativecontent

Why 7*6 matrix with 5 dimension has nul a =5. Shouldn't rank is 5 and nul is 1?

NhanNguyen-ftyt

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