Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy

Dimension of the Null Space or Nullity
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11:40 for Dimension of Null space, you're welcome

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[@tuyetlan888]

Hi there, I would like to know if I did exactly like you did in the video, except I put in row echelon form instead of a row reduced echelon form. Would I still be able to get the right answer?

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[@Car1ll]

Doesn't this mean that the dimension of A is equal to the number of collumns minus the number of rows of A. Since the reduced row echelon form will allways contain a number of pivots equal to the number of rows?

[@Robin-pc3jf]

Excellent video, though why does the calculation for nullspace start with B but end with A?

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ty

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[@yanyancui1601]

what if the free variable is not linearly independent?

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[@sanmvegs1641]

Let me ask you a question... is number of non pivot columns the nullity of a matrix and number of pivot columns is the rank of the matrix?

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When the pen hovers closely above the tablet, the mouse is responsive. You don't have to be in contact with it. I use one for Photoshop and that's how mine works.

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[@codex8538]

are the vectors associated with each free variable linearly independent always?

[@oneinabillion654]

Yes because only that vector associated with the free variable has a 1 in it, whereas it is 0 in the other vectors. So these vectors are always linearly independent after rref since theres no linear combination to represent that "1"

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[@howtoguro]

It actually doesn't need to be in RREF btw. REF will work better since it's a time saver. Row eschelon form is good enough because the numbers will change but the pivots will not. Since the rank-nullity theorem is dealing strictly with the # of pivots col and # of non-pivots col

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[@darlenemontesano3214]

how are x2, x4, x5 free variables?

[@GodsOfMW2]

If you look at the columns of the rref matrix, they do not contains any pivot ones. So if you were to expand the rref matrix, the free variables are the ones that appear in both equations.

[@nickchi8723]

basically the number of free varible in the matrix is the dimension of the null space. Dude why must linear algebra has so many terms. nullity = dimension of null space = numberof free verible in rref. Spend 10 min just want to know this and is at the last part of this video....

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