Question: Given the function f : R' - R', g(x, y) = (u, v) = (x -y, xy) (a) Compute the Jacobian matrix Jf(1, 1) and

Given the function f : R' - R', g(x, y) = (u, v) = (x -y, xy) (a) Compute the Jacobian matrix Jf(1, 1) and its determinant. a a (b) Compute the push-forward of each of tangent vectors ax' dy (c) Explain the significance of the sign of det Jf(1, 1). (d) Compute the pull back f* (du Adv). (e) Sketch the image R' of the rectangle R with corners at Pi (1, 1), P2(1.01, 1), P3(1.01, 1.02), PA(1, 1.02) and estimate the area of R'

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