ESM3A HW1 - Jacobs University Bremen School of Engineering...

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Unformatted text preview: Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 1 Issued: 8.9.2010 Due: Wednesday 15.9.2010 (in class) This homework deals with material that should be known from ESM2A/B. In particular, it dwells on eigenvalue/vector properties. Consult the textbook by Strang [S] (or any other text on the subject of matrix calculations and linear algebra) if you miss some knowledge. 1.1. Given is the 3 × 4 matrix A =   1 1 1- 1 3 1- 1 3 1 0- 1 2   . Find its rank (= dimension of the range space = maximal number of linearly independent columns = maximal number of linearly independent rows), and find the null-space (i.e., the space of all vectors x solving the homogeneous linear system Ax = 0). 1.2. Check that the three vectors u =   1 1 1   , v =   1- 1 1   , w =   1 i- 1   form a basis in the space IC 3 of complex 3-vectors. Express the canonical basis vectors in this basis, and find the complex matrix...
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ESM3A HW1 - Jacobs University Bremen School of Engineering...

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