Question

1. Let V be a vector space with dim V = 5. Fix two linearly independent vectors u, v ? V and set ? = {u, v}. Define W := span ? Determine which of the following statements are true/false. Circle the answer that best applies. (a) u and v are parallel. True False (b) W is a subspace of V. True False (c) W is a subspace of ??. True False (d) u = (x?, ..., x?) for some x?, ..., x? ? ?. True False (e) The set ? = (u, v) is an ordered basis for ?². True False (f) The set ? = (u, v) is an ordered basis for W. True False (g) W is a 2-dimensional subspace of V. True False (h) W is a subspace of ?². True False (i) For w ? W we have [w]? ? ?². True False (j) [u + v]? = [1 1]? True False

          1. Let V be a vector space with dim V = 5. Fix two linearly independent vectors u, v ? V and set ? = {u, v}. Define
W := span ?
Determine which of the following statements are true/false. Circle the answer that best applies.
(a) u and v are parallel.
True False
(b) W is a subspace of V.
True False
(c) W is a subspace of ??.
True False
(d) u = (x?, ..., x?) for some x?, ..., x? ? ?.
True False
(e) The set ? = (u, v) is an ordered basis for ?².
True False
(f) The set ? = (u, v) is an ordered basis for W.
True False
(g) W is a 2-dimensional subspace of V.
True False
(h) W is a subspace of ?².
True False
(i) For w ? W we have [w]? ? ?².
True False
(j) [u + v]? = [1 1]?
True False

1. Let V be a vector space with dim V = 5. Fix two linearly independent vectors u, v ? V and set ? = u, v. Define
W := span ?
Determine which of the following statements are true/false. Circle the answer that best applies.
(a) u and v are parallel.
True False
(b) W is a subspace of V.
True False
(c) W is a subspace of ??.
True False
(d) u = (x?, ..., x?) for some x?, ..., x? ? ?.
True False
(e) The set ? = (u, v) is an ordered basis for ?².
True False
(f) The set ? = (u, v) is an ordered basis for W.
True False
(g) W is a 2-dimensional subspace of V.
True False
(h) W is a subspace of ?².
True False
(i) For w ? W we have [w]? ? ?².
True False
(j) [u + v]? = [1 1]?
True False

Added by Irene F.

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