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

It will not make or break your application even at top schools. People get admitted to Ivy+ all the time with B’s even in the subject of their prospective majors. Just as many with perfect grades and scores don’t get admitted. They will be looking at the far bigger picture and signs of exceptionalism and not focusing on every individual grade.

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