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# hwB19 - (iii(4 pts Determine the projection ˆ s of s onto...

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ENEE 241 02 * HOMEWORK PROBLEM 19 Due Mon 03/24 Consider the complex-valued matrix V = £ v (1) v (2) v (3) / given by V = 3 a + jb 6 j 6 j 3 a + jb a + jb 6 j 3 (i) (4 pts.) Determine the only pair of real values a and b such that the columns of V are orthogonal. For those values of a and b , what are the resulting column norms? ( You may want to check your answer in MATLAB using V’*V before proceeding further .) (ii) (4 pts.) 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) . ( Gaussian elimination is not needed here.
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Unformatted text preview: ) (iii) (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 ? In what follows, we consider the complex-valued vectors x = 1 2 v (1)-1 2 v (2) + 3 v (3) y = 2 v (1) + 3 2 v (2)-v (3) (iv) (8 pts.) Without performing any complex computations , determine: • k x-y k 2 • the real value λ such that λ x is the projection of y onto x ....
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