For the mappings below state the domain and codomain determi

For the mappings below, state the domain and co-domain, determine whether or riot the mapping is linear, and if it is linear, compute the matrix representation. a) f (x_1, x_2) = (x_2, x_1) b) f(x_1, x_2) = x_1 x_2 c) f(x_1, x_2, x_3) = (x_1 + x_2, x_2 + x_3) d) f(x_1, x_2) = (sin x_1, cos x_2) e) f(x_1, x_2) = (x_1, 1)

Solution

a) f(x1,x2) = (x2,x1 )

domain = R^2 as it consists of ordered pairs (x1 and x2 )

codomain = R^2 as it consists of ordered pairs (x1 and x2 )

b) f(x1,x2) = x1x2

domain = R^2

codomain = R^2

c) f(x1,x2,x3 ) = (x1+x2 , x2+x3 )

domain = R^3 ( 3 variables )

codomain = R^3 ( 3 variables )