Would anyone happen to be good with linear algebra?

Should I bump the math help thread for you guys? >_>

In 2a, you're looking for a transformation matrix T(x) such that T(x) = A*x.

[SPOILER=WARNING: I haven't done linear algebra in a long time, so this is mostly BSing it =P]This is most likely not the proper way to solve the problem, but it solves it nonetheless.

Code:

┌       ┐┌   ┐   ┌   ┐
│ a b c ││ x │   │ m │
│ d e f ││ y │ = │ n │
│ g h i ││ z │   │ o │
└       ┘└   ┘   └   ┘

Inputs:
f(1, 0, 1)
f(1, 2, 1)
f(1, 0,−1)

Equations:
a + c = 1
a + 2b + c = 0
a - c = 0

d + f = 0
d + 2e + f = 1
d - f = 0

g + i = 0
g + 2h + i = 0
g - i = 1

Proposed solution:
    ┌         ┐┌   ┐   ┌   ┐
    │ 1 -1  1 ││ x │   │ m │
½ * │ 0  1  0 ││ y │ = │ n │
    │ 1  0 -1 ││ z │   │ o │
    └         ┘└   ┘   └   ┘