When solving examples that ask me to find a basis for the null, row or columnspace for a matrix I often get a different basis than what I find in the answer sheet. I know you can come up with many different bases for any given vector space so my answers can still be correct, I just have to make sure I made no mistakes. What I'm unsure about is if the basis I come up with can be composed of a different number of elements than what the answer sheet shows in it's solution and still be a correct answer.
2026-03-25 01:34:53.1774402493
null,row and column space can have different bases
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No, that cannot happen. Any two bases of a vector space have the same number of elements. That's a standard Linear Algebra theorem.