Final answer:
To find the inverse of a linear transformation, express the equation in terms of the output variables, y₁ and y₂, instead of the input variables, x₁ and x₂. Swap the roles of y₁ and x₁ and express y₁ in terms of y₂ and x₂. The resulting equation represents the inverse of the linear transformation.
Step-by-step explanation:
In order to find the inverse of a linear transformation, we need to express the given equation in terms of the variables in the output (in this case, y₁ and y₂) rather than the input variables (x₁ and x₂).
Starting with the equation y₁y₂ = 6x₁ - 29x₁ - 1x₂ + 5x₂, we can rewrite it as y₁y₂ = (6 - 29)x₁ + (-1 + 5)x₂, which simplifies to y₁y₂ = -23x₁ + 4x₂.
Next, we can swap the roles of y₁ and x₁ and express y₁ in terms of y₂ and x₂:
x₁ = (-23y₁ + 4x₂)/y₂.
This equation represents the inverse of the given linear transformation.