To answer this question we will use the following properties of vectors:
[tex]\begin{gathered} a=, \\ +=. \end{gathered}[/tex]Substituting u=<2,1> and v=<5,3> in the given expression we get:
[tex]2<2,1>-3<5,3>.[/tex]Applying the first property we get:
[tex]\begin{gathered} \lt2*2,2*1\gt+\lt(-3)*5,(-3)3\gt, \\ <4,2>+<-15,-9>. \end{gathered}[/tex]Applying the second property to the above result we get:
[tex]\begin{gathered} <4-15,2-9>, \\ <-11,-7>. \end{gathered}[/tex]Answer:
[tex]<-11,-7>.[/tex]