Linear Algebra 34 | Range and Kernel of a Matrix

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Комментарии
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I was literally thinking about kernels right when I saw that this video had just been uploaded four minutes ago.

MichaelWilliams-owue
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Sorry I didn't get what to prove where ran(A)=span(a1, ..., an). Is it not just a definition? Because the range define as Ax is the linear combination of the columns of A with x in the domain (Rn). And the span it's just the set of vector u in Rn (if M is in Rn) such that there are lambdas_j in R and u_j in M where every u can be write as a linear combinations of another vectors u_j. So the u_j are the a_1, ..., a_n and the lambdas are the x_i, ..., x_n so every vector u can be write as linear combination of the vectors of A. Am I correct?

Mmm! Also if A is not Linear independent suppose Rk with k<n, then their linear transformation is goint to generate a space in Rk but their span would do the same because some vectors are just redundant. And if A is linear independent the same. Maybe the proof come from this way?

And another doubt (maybe a fool one) did you draw the ker(A) and ran(A) as lineas because of something special?

MrWater
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What is name of your whiteboard you use ?

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