Null Space 3: Relation to Linear Independence

Understanding how the null space of a matrix relates to the linear independence of its column vectors

Category:

Education

Tags:

• nullspace
• null
• space
• subspace
• matrix
• vector

[ionglacier]

why does it only takes you to perfectly explain an entire lecture worth of information in 11min while my prof takes an hour and a half to explain the same thing which is also not as clear? lol great videos

[Argonaut1337]

Keep going on these Linear Algebra videos they're very good....

[leecristy]

@Formslip This is called proof!

[elai808]

Most enlightening 11 min of linear algebra I have ever seen. thank you SO MUCH!

btw. does this mean that any linearly independent matrix that is row reduced will equal its:Identity matrix?.. and that the dim of the NUL of the matrix must always = 0, therefore the dim of Col(A) must equal = the n number of columns which also equals the of rank(A)?

[Formslip]

why does it take 12 minutes to say the same thing over and over and over? i kept thinking we were getting to a point so i watched the whole thing

I GET IT

if the vectors in A are lin. indep.

N(A) = {0}

thats all this video says, move along

[mujuranokamen]

@pedroissler Man, I have to disagree. I'm not even in college, but I know derivatives, integrals, and now i'm learning linear algebra all thanks to Sal. I think this videos could substitute teachers "in real life".

[lightfireme]

@pedroissler I'm sorry, but I disagree with you. Some teachers explain math in an extremely technical way, making it hard for students that aren't math savvy to understand. And heck, some teachers are just lousy. I think Sal is extremely clear and informative in his delivery.

[pedroissler]

@ionglacier Don't demean your teacher. You were only able to understand it in 11 minutes and clearly because you went through one and a half hour of cramming with your teacher.. These videos are good to revise but in no way substitute your teacher..

[eongreen22]

@tareqhardan if you're talking about the nullspace being the zero vector, then that means that the columns of the original matrix are linearly independant

[xmoe4lifex]

i jus might nt fail my linear algebra exam tmmrw.......u should cm teach at the university of toronto. :)

[ummcloug]

Thank you so much! I have a final soon and I was having trouble learning from a book. Thank you!