Question: 12. Let X1, . .., *m ( R. If V is a subspace of R that includes X1, . .., Am, is span {x1, .

12. Let X1, . .., *m ( R". If V is a subspace of R" that includes X1, . .., Am, is span {x1, . .., I'm} always a subspace of V? Is V always a subspace of span{x1, ..., Xm}? Explain why or find counterexamples. MATH 203: Linear Algebra Holly Miller and Violet Nguyen 13. Let W = span (i ) . (9 . (3.)} (a) Is W a subspace of 3? (b) Is the set linearly independent? (c) Find a basis for W. 14. Find an example in R4 of each of the following: (a) a set of linearly independent vectors that do not span R4, (b) a set of linearly dependent vectors spans R4, (c) and a set of linearly independent vectors that span R4. 15. For what constants c is the set {(2) . ( linearly independent? 16. Find a set of 3 vectors in R2 that are linearly independent, or explain why it is impossible. 17. Can a set of 5 polynomials from P3 be linearly independent? Explain why or why not. 18. Let W be a 2-dimensional subspace of V. Is it possible for (a) I to be 1-dimensional, (b) V to be 3-dimensional, (c) or V to be infinite-dimensional

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