Dimension of the column space or rank | Vectors and spaces | Linear Algebra | Khan Academy

Dimension of the Column Space or Rank

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[matthewfedoseev]

"The rank of a matrix is the number of linearly independent column vectors that can be used to construct all of the other column vectors."
Perfect. Thank you so much!

[andy]

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[nereaelizaldeojembarrena]

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[hahaeliz]

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[Maverick.]

dim(null space)=number of non pivoted columns where as dim(column space)= number of pivoted columns.
very nicely explained thank you

[thevadidekizambak]

that video will definitely help me in my final exam tomorrow. thank you!

[shamrick]

this video lecture help to learn to basis, rank and dimension for the subspace of column vector which i did not find a good one anywhere. thank you

[scottySK]

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[verelanz]

i love you, man...
this is the first time i really understood everything someone told me about this stuff

[PKDana]

K I watched some videos, and I think it's what I said, except you do not go back to the original un-reduced matrix to find the linearly independent rows that comprise the basis for the row space of A: you just use those rows you found in the reduced form. Nicely, once you find the row/column space, it is an easy task to find the column/row space, since the reduction exposes both in the matrix.

[ishansrt]

You are simply charming.saved my quiz day. Thank you

[emreer]

thanks a lot, that helped me a lot before my final ! 

[georgechisanga]

thanks for making "ranking" easy for me to understand,