Inverse transformation for linear transformations

[SteelDirigibl]

Homework Statement

Find the inverse transformation T^-1(x, y) in each case below:

(a) T(s,t) = (3s+t, s-2t)
(b) T(s,t) = (s³, s+t)
(c) T(s,t) = (t, s)
(d) T(s,t) = (e^t, s)

The Attempt at a Solution

I'm not completely sure what this is asking. What is an inverse transformation? I'm sure it's really basic, I just can't find an explanation online. The only examples I can find have one variable. So I can't really get anywhere on this.

 

[Mark44]

A transformation is a kind of function. Instead of mapping one number to another as ordinary functions do, it maps a vector to some other vector, possibly in a different vector space.

For example, if s = 2 and t = 1, the transformation in part a maps the vector <2, 1> to the vector <7, 0>. The inverse transformation, T^-1 would map <7, 0> back to <2, 1>.

If a transformation is linear (as a and c are), there is a matrix that represents the transformation. The ones in b and d are nonlinear, so "finding the inverse transformation" might involve only describing what the inverse transformation needs to do.