Consider the mapping f : R2 -> R2 given by f(x, y) = (x2 – y’, 2xy). (a) Compute the Jacobian matrix of f at P = (4, -7), i.e. Df(P). (b) Show that the Jacobian matrix found in part (a), when view a linear transfor- mation of R’ to itself, preserves angles between vectors, i.e.

Consider the mapping f : R2 -> R2 given by f(x, y) = (x2 – y’, 2xy).
(a) Compute the Jacobian matrix of f at P = (4, -7), i.e. Df(P).
(b) Show that the Jacobian matrix found in part (a), when view a linear transfor-
mation of R’ to itself, preserves angles between vectors, i.e.
(Df(P)u) .(Df(P) v)
1-V
I Df(P)u|| DS(P)v|
(c) Show that this property of the Jacobian matrix of f holds for all point P on the
plane not just P = (4, -7). Remark: f is called a conformal transformation.

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