EDB — 1V0

Exercises

1. [1V0] Topics:matrix, determinant. Note:exercise 4 in the pseudo-homework of 14/3/2013.

   1. Let \(A∈ℝ^{2× 2}\) be a 2 by 2 matrix. Identifying \(ℝ^{2× 2}\) with \(ℝ^{4}\), calculate the gradient of the determinant, and verify that it is nonzero if and only if the matrix is nonzero.

   2. Let \(Z\) be the set of matrices \(ℝ^{2× 2}\) with zero determinant. Show that it is a closed set with an empty interior.

   Solution 1

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