Rank & Nullity; How to Find a Basis for Null Space and Column Space [Passing Linear Algebra]

What is a Basis: • What is a Basis for a ...
What is Null Space: • What is Null Space? Ge...
The Column Space of a matrix is the span of the columns of the matrix.
The Null Space of a matrix, A, is the collection of all x vectors that satisfy Ax=0.
Rank is the dimension of the column space
Nullity is the dimension of the null space
Rank of A + Nullity of A = number of columns of A
Video Guide:
How to find basis for Col(A): 0:55
How to find basis for Nul(A): 2:28
What is Rank and Nullity: 7:20
Rank/Nullity Theorem: 8:51

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[@karimabouelela3665]

I believe there is a small mistake instead of 7 it should be -3

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[@mo100saad]

Small error 3:52 , the first row should be [1 0 4 -3]

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[@man9mj]

before watching this video, I watched around 10 videos about null space and column space trying to understand or know the difference. Your explanation made the difference very clear. Thanks brother.

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[@EgonuPatrick]

Why are you using the elements of the row reduced echelon form as the basis of the nullspace and yet you said you go back to the original matrix

[@rudolphtaflev8251]

is 12 a pivot?

[@cloak-and-daggersdad4921]

Yep

[@mazharulhaque2468]

Note: "The N(A) is a plane but it's in R4, but the C(A) is also a plane, but it's in R3." Interesting, it's because it's a 3x4 matrix.

[@cristianbotello9543]

12 isnt a pivot...... it has to a 1

[@cloak-and-daggersdad4921]

12 is a pivot because the number below it are all zero........ For it to be pivot it doesn't have to be always 1...the only thing it need is all the numbers numbers below it should be 0...i hope I make sense 8)

[@kayanhaider50]

The pivots only need to be 1 in RREF not REF