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So I'm studying for my test tomorrow and I understand how to find the dimensions of ColA and NulA, but what I don't understand is when they give you for example a matrix H, and then they just say Find dimH.

What am I suppose to be solving for? We did two examples in class and in one question my teacher obviously solved for the dim of the column space, and in the second question she solved for the dimension of the nul space.

So when do you solve for each and how do you know which one to solve for?

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Secondly, I've seen a question that says "when does (a value) in the set (v1, v2, v3) not form a basis for R^3?" and the idea here was that you had to solve so that the determinate was not equal to 0.

DOes this have something to do with the IMT stating that detA cannot = 0 for a matrix to be invertible and thus cannot be a basis?I'm kind of confused on the relationship here between the determinate and whether or not it is a basis.

Thanks,

Elliott

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# Find dimH

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