MAT 223 Winter 2023
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MAT 223
Winter 2023
1. Let S = { v⃗1 , v⃗2 , v⃗3 } be a subset of R3 . Explain how to show whether the set S is linearly independent or linearly dependent. Use your own specific example(s) in your explanation.
2. Give an example of a set X and a vector 
in R2 such that projX 
does not exist (i.e. does not make sense mathematically). Explain your thinking and use a diagram or graph.
3. Find an example of a basis for R3 , B = {b⃗1 , b⃗2 , b⃗3 }, that does not contain any standard basis vectors. Explain your thinking.
4. Let S be a subset of Rn . Explain in your own words how you show S is a subspace using the definition of subspace.
5. Let P be the plane given by:
Prove P is a subspace using the definition of subspace.
6. Let S be a subset of Rn . For which choices of S is span(S) a set with infinitely many vectors? Justify your conclusion.
2023-03-04