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I know this is a basic concept but I don't really understand it. I don't get what the difference between rank and dimension is. According to my book, the rank of a matrix is the dimension of the column space. Does that not imply that they are the same, unless the question specifically states they are different? And how would I be able to even tell if they are different unless it tells me?

Confusing to me to say the least.

Thanks.