Am I allowed to solve matrix multiplication that involves matrices who depend on individual components of an array

If this is possible, how do I approach it?

If I have an array of values i.e.

w = [1 2 3 4]

and want to multiply matrices who are functions of w to then arrive to an array of solutions i.e.

a = [f_1(w) f_2(w); f_3(w) f_4(w)]
b = [f_5(w) f_6(w); f_7(w) f_8(w)]
c = a*b
mag = [norm(c(1)) norm(c(2)) norm(c(3)) norm(c(4))]

where c(1) is a function from w(1), c(2) is a function of w(2), and so forth

I keep receiving an error where b in this case would be not result in many 2x2 matrices but instead turns into a one big 2x# matrix. End goal is to plot w and mag.