As per given by the question,
There are given that,
[tex]u=<5,\text{ -1>, v=<-2, 1>, w=<-1, 0>}[/tex]Then find the value of;
[tex]2u-3(v-w)[/tex]Now,
If u=<5, -1>, then 2u is;
[tex]\begin{gathered} 2u=2(5,\text{ -1)} \\ =(10,\text{ -2)} \end{gathered}[/tex]If, v=<-2, 1>, and w=<-1, 0>, then 3(v-w) is;
[tex]\begin{gathered} 3(v-w)=3((-2,\text{ 1)-(-1, 0)} \\ =3(-2+1,\text{ 1-0)} \\ =3(-1,\text{ 1)} \\ =(-3,\text{ 3)} \end{gathered}[/tex]Now,
Put the value of 2u and 3(v-w) in given function 2u-3(v-w),
So,
[tex]\begin{gathered} 2u-3(v-w)=(10,\text{ -2)-(-3, 3)} \\ =(10+3,\text{ -2-3)} \\ =(13,\text{ -5)} \end{gathered}[/tex]So, the value of given function 2u-3(v-w) is <13, -5>.
Hence, the option C is correct.