Linear Algebra 7g: The Nullspace of a 3x3 Matrix with a Specific Pattern

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Firstly, thank you so much for these videos. But, one thing, you started with geometrical, polynomial and real number vector spaces. Then you showed the first null space example of some geometrical vectors, which was the linear combination of linear combinations of those vectors that yield zero vector.

But in this video and the previous video, you are analyzing the null space of a given matrix. I do not understand the relation between those three types vectors with these matrices. So, what does it really mean to find out the null space of a given matrix in terms of those (geometrical, polynomial and real number) vector spaces?

I apologize if the question is a rather stupid one. I really appreciate these videos of yours. Thank you again.

RUMI
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If entires r1c2 and r1c3 also happen to share the linear dependences of the sub columns below them won't the first entry in the null vector need to be set to '0' (i.e. 'nothing to add or subtract')?

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