(For those who have studied multivariable calculus.) Let T be an invertible linear transformation f…

(For those who have studied multivariable calculus.) Let T be an invertible linear transformation from ℝ^2 to ℝ^2 represented by the matrix M. Let Ω_1 be the unit square in ℝ^2 and Ω_2 its image under T. Consider a continuous function f(x, y) from ℝ^2 to ℝ, and define the function g(u, v)=f(T(u, v)) . What is the relationship between the following two double integrals? ∬_Ω_2 f(x, y) d A and ∬_Ω_1 g(u, v) d A Your answer will involve the matrix M. Hint: What happens when f(x, y)=1, for all x, y ?

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Видео (For those who have studied multivariable calculus.) Let T be an invertible linear transformation f… канала Sammy Lauren