Practical Linear Algebra: A Geometry Toolbox, Third edition
Gerald Farin & Dianne Hansford
CRC Press, Taylor & Francis Group, An A K Peters Book, 2013

Linear Combinations
Input vector a is blue;
Input vector b is green;
Result of the linear combination is red. 
result vector = s*a + t*b

Note that as we change s, the result changes parallel to a, and as we change t, it changes parallel to b.

(* Input vectors *)
(* Select a set and load into a,b *)
a0 ={1,0};  b0 ={0,1};
a1={2,1};  b1 ={-2,1};
a = a1;   (*in blue *)
b= b1;  (* in green *)

(* create a range for plotting *)
lgth = Norm[a];
If[Norm[b] > lgth,lgth = Norm[b]];

(* graphics entities for input vectors *)
arrowa={Arrowheads[Large],Arrow[{{0,0},a}]};
arrowb ={Arrowheads[Large],Arrow[{{0,0},b}]};

Manipulate[
Graphics[{Blue,arrowa, Green,arrowb,Red,{Arrowheads[Large],Arrow[{{0,0},s*a+t*b}]} },PlotRange->{{-lgth,lgth},{-lgth,lgth}}],{{s,0.5},-1,1},{{t,0.5},-1,1}, Alignment->Left,FrameLabel->{" "," ","red = s*blue + t*green"," "}]