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

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Advance Math

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

PART A Fill in the blank. Select “A” for Always, “B” forSometimes, 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)_ abasis for V.

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

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

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

    expressed uniquely as a linear combination of vectors in S.

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