An answer wnthoul wrlel won wll get no credit. e your final answer. is a take-ho

Question

An answer wnthoul wrlel won wll get no credit. e your final answer. is a take-home quiz. You should complete this quiz without an dicate y assistand r from inanimate sources like the web or printed resources. The quiz is due . the next class. Consider the set S = 0 | 1 | ,V 1. Find a vector v so that span(S) has dimension 3 and justify your answe 2. Find a vector v so that span(S) has dimension 2 and justify your answe 3. Explain why it is not possible to find a vector v so that span(S) has din sheets 267cm x

Explanation / Answer

Apparently, S is a subset of R3. Further, span (S) contains all the linear combinations of the vectors (1,0,0)T,(0,1,0)T and v. If dim(span(S)) is 3, then v must not be a linear combination of (1,0,0)T and (0,1,0)T. Thus, v = (a,b,c)T, where a,b,c are real numbers and c 0. span (S) contains all the linear combinations of the vectors (1,0,0)T,(0,1,0)T and v. If dim(span(S)) is 2, then v must be a linear combination of (1,0,0)T and (0,1,0)T. Thus, v = (a,b,0)T, where a,b are arbitrary real numbers. This part of the question has got truncated. However, regardless of the value of v, dim(span(S)) 2 as the vectors (1,0,0)T and (0,1,0)T are linearly independent. If v is a linear combination of (1,0,0)T and (0,1,0)T, then dim(span(S)) = 2,otherwise, dim(span(S)) =3.

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