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State whether each of the following statements is (always) true, or is (possibly) false, in the box after the statement.
State whether each of the following statements is (always) true, or is (possibly) false, in the box after the statement. If the statement is false, an explicit number must be give - with numbers, matrices, or functions, as is appropriate. If it's always true, give a clear explanation.a) If {v1, v2, v3} is linearly independent in R3, then {v1, v2} is linearly dependent in R3.b) If {v1, v2, v3} spans a subspace U of a vector space V, then dim(U) is bigger than or equal to 3.c) {[a b c d]E M2,2 (R) |a+b+c=0} is a subspace of M2,2(R)d) The set of {f E F(R) |f(2)=1} is a subspace of F(R)={f |f : R -> R}.
