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False, (If two or more of the equations in the system are inconsistent, then the system does not have any solutions.)

False,(Same explanation as 1)

False,(A system of consistent linear equations with more variables than equations has more than one solution)

True,(A linear system for which the number of equations is the same as the number of variables can be consistent or inconsistent. It has one solution if it is consistent and no solutions if it is inconsistent)

True,(Proof can be more complicated, contact me if needed)

True,(A linear independent set can have at most the same number of elements as the dimension of the space they are in)

False,(It is not necessary for one of them to be the zero vector, for example: In R2 the vectors (1,1) and (3,3) are dependent and neither is the 0 vector)

False,(If they are linearly INDEPENDENT then none of them can be multiples of the others)

True

Please let me know if you need any clarification. I'm always happy to answer your questions.