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Find the inverse of the linear transformation y₁y₂ = 6x₁ - 29x₁ - 1x₂ + 5x₂.

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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.

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