We are given the following two vectors
[tex]\begin{gathered} a=<1,-4> \\ b=<2,5> \end{gathered}[/tex]We are asked to find the following
[tex]-2a+5b[/tex]First, multiply the vector a with the scaler -2 to get -2a
[tex]\begin{gathered} -2a=<-2\cdot_{}1,-2\cdot-4> \\ -2a=<-2,8> \end{gathered}[/tex]Now, multiply the vector b with the scaler 5 to get 5b
[tex]\begin{gathered} 5b=<5\cdot2,5\cdot5> \\ 5b=<10,25> \end{gathered}[/tex]Finally, add -2a and 5b to get -2a+5b
[tex]\begin{gathered} -2a+5b=<-2,8>+<10,25> \\ -2a+5b=<-2+10,8+25> \\ -2a+5b=<8,33> \end{gathered}[/tex]Therefore, the resultant vector in component form is
[tex]-2a+5b=<8,33>[/tex]