## Elementary Linear Algebra 7th Edition

$S$ 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.