State whether each of the following statements is (always) true, or is (possibly

ID: 3420989 • Letter: S

Question

State whether each of the following statements is (always) true, or is (possibly) false, in the box after the statement.

• If you say the statement may be false, you must give an explicit example - with numbers, matrices, or functions, as is appropriate!

• If you say the statement is always true, you must give a clear explanation.

a) If {v1, v2, v3} is linearly dependent in R3 , then {v1, v2} is also linearly dependent in R3.

b) The set of polynomial functions : {1 + ax2 | a R} is a subspace of F(R) = {f | f : R R}.

c){ [ a b

c d ] M2,2(R) | a + d = 0} is a subspace of M2,2(R).

d) if v1,v2, v3, and v4 are linearly independent vectors in a vector space V, then dim(V)=4

State whether each of the following statements is (always) true, or is (possibly

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