Chapter 4 - Vector Spaces - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 32

$S$ is a linearly dependent set of vectors.

Since one can have the combination $$(2,-1)=3(1,0)-(1,1)$$ then we get the non trivial combination $$(2,-1)-3(1,0)+(1,1)=(0,0).$$ Hence, $S$ is a linearly dependent set of vectors. Or, instead, since $R^2$ has dimension $2$ then the maximum number of linearly independent vectors is $2$ but $S$ has $3$ vectors then it must be linearly dependent.