ENEE241hw06

ENEE241hw06 - ENEE 241 02 HOMEWORK ASSIGNMENT 6 Due Tue...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 6 Due Tue 03/15 Problem 6A Consider the complex-valued matrix V = ± v (1) v (2) v (3) v (4) ² = 23 + jc - 8 a + jb a + + - 8 - 8 a + + 3+ - 8 a + 2 (i) (6 pts.) Show that there exists only one choice of constants a R , b R and c> 0 such that the columns of V are pairwise orthogonal. For that choice of a , b and c , what are the resulting column norms? ( You will need to set two column inner products equal to zero. Check your answers in MATLAB using V’*V before proceeding further .) From now on, assume that a , b , c and d are as found in part (i) above. (ii) (6 pts.) Determine d such that the real-valued vector s = ± 27 45 41 23 ² T equals Vd .( Gaussian elimination is not needed here. Again, verify your answers in MATLAB. ) (iii) (5 pts.) Determine the projection ˆ s of s onto the subspace generated by the vectors v (2) and v (4) . What is the value of ± s - ˆ s ± 2 ? (iv) (3 pts.) If x = v (1) +2 j v (2) + v (3) j v (4) y = j v (1) - 3 v (2) - 3 v (3) + j v (4) determine ± x - y ± 2
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ENEE241hw06 - ENEE 241 02 HOMEWORK ASSIGNMENT 6 Due Tue...

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