ENEE241hw05

# ENEE241hw05 - ENEE 241 02 HOMEWORK ASSIGNMENT 5 Due Thu...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 5 Due Thu 03/12 You should not use matrix functions on your calculator (or MATLAB). Show all intermediate steps. Let v (1) =[2 - 54 - 2] T , v (2) =[1 2 1 - T and v (3) =[3 0 - 11 ] T . (i) (3 pts.) Show that v (1) , v (2) and v (3) are (pairwise) orthogonal, and compute their norms. In what follows, let s = [ 22 1 54 54 ] T . (ii) (3 pts.) Determine the projection f ( i ) of s onto each v ( i ) (where i =1 , 2 , 3). (iii) (2 pts.) Determine the angle between s and v (1) . (iv) (3 pts.) Determine the angle between s and the plane deFned by v (2) and v (3) . (v) (3 pts.) Determine the projection g of s onto the three-dimensional subspace deFned by v (1) , v (2) and v (3) . (vi) (2 pts.) Verify that error vector s - g is orthogonal to each of v (1) , v (2) and v (3) . (vii) (4 pts.) Solve the system 2131 - 5 2 0 22 41 - 1 51 - 2 - 2 1 48 d 1 d 2 d 3 d 4 = 38 27 50 46 without using Gaussian elimination. ( Hint: What is the relationship between s - g and the fourth column of the matrix above? ) Solved Examples S 5.1 ( P 2.24 in textbook). Consider the four-dimensional vectors a =[ - 1724 ] T and b =[30 - 1 - 5 ] T . (i) Compute

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ENEE241hw05 - ENEE 241 02 HOMEWORK ASSIGNMENT 5 Due Thu...

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