Finding Basis for the Column Space of a Matrix | Linear Algebra

We use elementary row operations to reduce a matrix to row echelon form in order to find a basis for the column space. After completing this process, the columns containing the leading 1s correspond to column in the original matrix which form a basis for the column space, col(A). Thus, the number of row vectors that have those leading 1s, which is the rank of the matrix, is also the dimension of the column space, since each leading 1 indicates a column of the original matrix that is in the basis of the column space. Again, recall a basis for the column space is a set of linearly independent column vectors that span the column space. #linearalgebra #matrices

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[WrathofMath]

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[math-rg]

What a clean and clear shot... wow... just 3 mins to understand such a complex thing... thank you

[migui]

short, clear, got the info i wanted, great video

[RaunakAnwar-be]

I love how simple and straightforward your video is on this exact subject regarding column spaces. Almost every video I have seen on column spaces is super long (at least 10-15 mins) and just too overcomplicated.

[BARODI]

thank you master it was very clear just taking 4 minutes to understand rather than spending 1 whole hour in class with only 3 hour of sleep

[mrzackmorris]

Love your intro here haha. Great Vid bro Thank you for the concise info

[mantisynth]

you explained in perfect clarity what i couldn't understand after rereading our useless textbook for over an hour. thank you so much

[JD-cirs]

This is incredible. Thank you very much. I hope you gain more viewership.

[selindoga]

Hi friend, you just solved my life problem in minutes. Thank

[JohnnyNavarro]

dude...Thank you! you made that so simple

[anwesha]

Thank you so much master for the great explanation!

[tintprxy]

I’m trying to prepare for this test but the intro had me laughing for at least 30 secs 😭

[averageotter]

So as a clarification the three vectors c1 c3 c5, form a basis for the colspace. This in turn means that the Span of (c1 c3 c5) is the col space?

[alitgm]

i still dont get the difference between the basis and generating set are they the same thing ????

[nova_sw]

Bro Lovee you so much for this one😭😭 really helped me thanks

[abanana_]

Wait so its just any column in the form that has a 1 in it or do the ones have to be in different rows?

[RahulDabas-qfox]

Hey mate i wanna ask will here dimension=3 is defined of A or col(A)

[JohnKale-offz]

Are leading ones the same thing as pivots?

[Bedoroski]

I have a question: when finding the Row/Column space, when can we swap rows so not to change to Row/column space of the original matrix

[sagar]

Thank you white man. This helped me with my exams