hwB18 - ENEE 241 02 * HOMEWORK PROBLEM 18 Due Fri 03/14...

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Unformatted text preview: ENEE 241 02 * HOMEWORK PROBLEM 18 Due Fri 03/14 Consider the 4 3 matrix V = v (1) v (2) v (3) / given by V = - 1 . 3702 4 . 6799- . 6379 1 . 8877- 2 . 5466 4 . 7986 2 . 0596- 5 . 5447- 2 . 1429- 2 . 5134 3 . 7242- . 9872 (i) (3 pts.) Compute (e.g., in MATLAB) the inner product matrix V T V , rounding to four significant digits. (ii) (8 pts.) Obtain (by hand) 3 3 matrices D (diagonal with positive entries) and U (upper triangular with unit diagonal entries) such that V T V = U T DU (iii) (9 pts.) Determine (by hand) coefficients c ij that yield orthonormal vectors w (1) , w (2) and w (3) , where: w (1) = c 11 v (1) w (2) = c 12 v (1) + c 22 v (2) w (3) = c 13 v (1) + c 23 v (2) + c 33 v (3) Solved Examples S 18.1 ( P 2.39 in textbook). Consider a n 3 real-valued matrix V = v (1) v (2) v (3) / which is such that V T V = 16- 8- 12- 8 8 8- 12 8 11 (i) Determine matrices D (diagonal with positive entries) and U (upper triangular with unit...
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hwB18 - ENEE 241 02 * HOMEWORK PROBLEM 18 Due Fri 03/14...

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