Will getting a B in math [linear algebra at a college] as a prospective math major hurt my chances at top schools?

Nothing you can do about it now, other than take a very close look at where you are applying. It appears that you’ve fallen into the “dream school” trap - you’re obsessed with one school that you think is perfect. I really hope that you’re making financial and academic safeties now. There are SO many schools where you can study math.

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