Linear algebra: T or F question. If its false, please provide a counter-example (not an explanation) show that it can be false. 1) Let S1 and S2 be sets of vectors. If Span(S1) = Span (s2), then S1 = S2. 2) A plane in R^3 is a two-dimensional subspace Solution 1) False Consider R2 One basis for R2 is S1={(1,0),(0,1)} Another basis is S2={(1,1),(1,0)} S1 and S2 are not equal but span(S1)=span(S2)=R2 2) True A plane is a subspace spanned by two linearly independent vectors.

1. Linear algebra: T or F question. If its false, please provide a counter-example (not an
explanation) show that it can be false.
1) Let S1 and S2 be sets of vectors. If Span(S1) = Span (s2), then S1 = S2.
2) A plane in R^3 is a two-dimensional subspace
Solution
1)
False
Consider R2
One basis for R2 is S1={(1,0),(0,1)}
Another basis is S2={(1,1),(1,0)}
S1 and S2 are not equal but
span(S1)=span(S2)=R2
2)
True
A plane is a subspace spanned by two linearly independent vectors