Answer to Question #119437 in Linear Algebra for Sourav Mondal

Question

Let f : R2-->R1be defined by
f(x1, x2) = (3x1+ 4x2)and T : R2--> R2be
defined by T(x1 , x2) = (x1- x2, x1+ x2).
Suppose g = f o T. What is g (2, 3) ?

Answer 1

$f(x_1,x_2)=3x_1+4x_2\\ T(x_1,x_2)=(x_1-x_2,x_1+x_2)\\ g(x_1,x_2)=f(x_1,x_2)\circ T(x_1,x_2)=\\ =3(x_1-x_2)+4(x_1+x_2)=7x_1+x_2\\ g(2,3)=7\cdot2+3=17$