hw10 - Solved Example S 16.1 The complex-valued matrix V =...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 10 Due Tue 03/24 Consider the complex-valued matrix V = £ v (1) v (2) v (3) / = 4 4 - 1 1 - 3 j 1 + 3 j 2 1 + 3 j 1 - 3 j 2 (i) (3 pts.) Evaluate the norms of the three columns v (1) , v (2) and v (3) . (ii) (4 pts.) Show that the three columns are mutually orthogonal. ( You may want to check your answers in MATLAB using V’*V before proceeding further .) (iii) (5 pts.) Determine c such that the real-valued vector s = £ 11 - 16 8 / T equals Vc . ( Gaussian elimination is not needed here. Again, verify your answers in MATLAB. ) (iv) (4 pts.) Determine the projection ˆ s of s onto the subspace generated by the vectors v (1) and v (2) . What is the value of k s - ˆ s k 2 ? (v) (4 pts.) If x = 1 2 v (1) + 1 2 v (2) - 3 2 v (3) y = v (1) - 3 2 v (2) + 5 2 v (3) determine the value of k x + 2 y k 2 without performing complex computations.
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Unformatted text preview: Solved Example S 16.1 The complex-valued matrix V = £ v (1) v (2) v (3) / = 3 a + jb 6 j 6 j 3 a + jb a + jb 6 j 3 (where a and b are real-valued) has pairwise orthogonal columns. (i) Determine a and b . What are the column norms? (ii) Express the complex-valued vector s = £-5-2 j-10 + 8 j 1-14 j / T as a linear combination of v (1) , v (2) and v (3) . (iii) If x = 1 2 v (1)-1 2 v (2) + 3 v (3) y = 2 v (1) + 3 2 v (2)-v (3) explain why the projection λ x of y onto x is such that λ is real. Determine λ without performing complex operations....
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This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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