Final answer:
To find the inverse of a linear transformation T1 : R2 → R2, solve the given equations for x and y in terms of a and b.
Step-by-step explanation:
To find the inverse of a linear transformation T1 : R2 → R2, we need to solve the equation T(x, y) = (2x + 7y, 6x + 22y) for x and y. Let's denote the inverse transformation as T⁻¹(x, y) = (a, b). We can set up the equations: 2x + 7y = a. 6x + 22y = b.
Now we need to solve these equations for x and y in terms of a and b. We can use matrix methods such as Gaussian elimination or inverse matrix to find the solutions. Solving the equations, we get: x = (22a - 7b) / 68. y = (2b - a) / 68. Therefore, the inverse transformation is T⁻¹(x, y) = ((22x - 7y) / 68, (2y - x) / 68).