Question

The answers are given already but can u pls give explanation on how they got each answer?

PART A Fill in the blank. Select “A” for Always, “B” for Sometimes, and “C” for Never.

1. A set of 3 vectors from R3 _S(B)_ forms a basis for R3.

2. A set of 2 vectors from R3 _N(C)_ spans R3.

3. A set of 4 vectors from R3 is _N(C)_ linearly independent.

4. A set of 2 vectors from R3 is _S(B)_ linearly independent.

5. If a set of vectors spans a vector space V then it is _S(B)_ a basis for V.

6. If B1 and B2 are two different sets of vectors and each forms a basis for the same vector space, then B1 and B2 _A_ have the same number of vectors.

7. If A is a set consisting of only the zero vector and V is a vector space, then A is _A_ a subspace for V.

8. If S is a linearly independent subset of a vector space V, then a given vector in Span(S) can _A_ be

   expressed uniquely as a linear combination of vectors in S.

Answer 1