don\'t have much time left because i have a midterm the same day, it would be mu

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don't have much time left because i have a midterm the same day, it would be much appreciated. thanks

Let f : Rn rightarrow Rn and g : Rn rightarrow Rn be inverse functions. Suppose f and g arc differentiable. Show that the determinants of Df and Dg are not 0, and that Dg = (Df) -1 Find the eigenvalues of A. For each eigenvalue, find an eigenvector having length one. Let B be the matrix whose rows arc the eigenvectors found in part (b). Show that B is an orthogonal matrix. Let f : Rn rightarrow Rn and g : Rn rightarrow Rn be inverse functions. Suppose f and g arc differentiable. Show that the determinants of Df and Dg are not 0, and that Dg = (Df) -1 Find the eigenvalues of A. For each eigenvalue, find an eigenvector having length one. Let B be the matrix whose rows arc the eigenvectors found in part (b). Show that B is an orthogonal matrix.

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