True-False for Quiz 3

[only the Ch. 3.1, 3.2 parts]

These are just for practice and don't affect your grade. I'm assuming you've read thru Leon Ch. 3.2. See his web site has more TF practice like this. Also try the other TF for Quiz 3 [Ch2], and the TF quiz on the help page.

Suppose that S is a finite set of vectors {v1, v2 ...vp} in a vector space V.

True False. If the span of {v1, v2 ...vp-1} is V, then S is also a spanning set of V.

True False. The set of all linear combinations of vectors in S is a subspace of V.

True False. If S Í T are sets in V, then span (S) Í span (T).

True False. P2 is a subspace of P3. (P3 = set of poly's of degree < 3).

True False. The set of 2x2 matrices, denoted R2x2, is a vector space.

True False. A set with only one vector must be independent.

True False. Any set including the vector 0 must be dependent.

True False. Row operations can change the nullspace of a matrix.

True False. Every plane is a subspace of R3.

True False. Is U and W are subspaces of V, then the union of U and W is, too.

Written by S.Hudson.

Back to Exam page