In each of the following statements, S is a subset of a vector space V, and each vector Ui represents a vector in V. In each statement, please assume that u1, U2, ... are all distinct vectors. At the...

Extracted text: In each of the following statements, S is a subset of a vector space V, and each vector Ui represents a vector in V. In each statement, please assume that u1, U2, ... are all distinct vectors. At the end of the statement, indicate whether it is true or false. 1. If S contains the zero vector, then S is linearly dependent. [ Select ] 2. If c1 = c2 = c3 = 1 is a solution to c1ui + c2 U2 + c3 U3 = 0, then S {u1, u2, U3} is linearly dependent. [ Select ] 3. If S is linearly dependent, then S contains the zero vector. [ Select ]