# (1 point) Suppose a change of coordinates T:R2→R2T:R2→R2 from the uvuv-plane to the xyxy-plane is given...

###### Question:

(1 point) Suppose a change of coordinates T:R2→R2T:R2→R2 from the uvuv-plane to the xyxy-plane is given by

x=4v−3u−1,   y=1+4u+2v.x=4v−3u−1,   y=1+4u+2v.

(a) Find the absolute value of the determinant of the Jacobian for this change of coordinates.

∣∣∣∂(x,y)∂(u,v)∣∣∣=∣∣∣det|∂(x,y)∂(u,v)|=|det
 ⎡⎣⎢⎢[ ⎤⎦⎥⎥]
∣∣∣=|=

(b) If a region D∗D∗ in the uvuv-plane has area 7.047.04, find the area of the region T(D∗)T(D∗) in the xyxy-plane.

Area =

A

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