Wvecmat10 - ECE 421 Sum 2010 Detailed Solutions Set 10 Vectors and Matrices 1 10-1 Let two vectors be b 1 = 2 1 1 1 ℄ T and b 2 = 2 3 1 1 ℄ T

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Unformatted text preview: ECE 421 - Sum 2010 Detailed Solutions - Set 10: Vectors and Matrices 1 10-1. Let two vectors be b 1 = [ 2 ; 1 ; 1 ; 1 ℄ T and b 2 = [ 2 ; 3 ; 1 ; 1 ℄ T and let the matrix B be defined as the matrix having b 1 and b 2 as columns. Compute the following: (a) b T 1 b 2 , (b) B T B , (c) BB T . DETAILED SOLUTION: In the solutions below, the matrix B is defined as the matrix having b 1 and b 2 as columns. Using b 1 and b 2 as defined in the problem statement this produces B = ¢ b 1 b 2 £ = 6 6 4 2 2 1 3 1 1 1 1 7 7 5 a (a) Compute b T 1 b 2 . With b 1 and b 2 as defined in the problem statement, b T 1 b 2 is given by b T 1 b 2 = [ 2 ; 1 ; 1 ; 1 ℄ 6 6 4 2 3 1 1 7 7 5 = 2 2 1 3 1 1 1 1 =-7 b (b) Compute B T B. Using the definition of the matrix B as defined in equation a we have B T B = 2 1 1 1 2 3 1 1 6 6 4 2 2 1 3 1 1 1 1 7 7 5 = 7 7 7 15 c (c) Compute B B T ....
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.

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Wvecmat10 - ECE 421 Sum 2010 Detailed Solutions Set 10 Vectors and Matrices 1 10-1 Let two vectors be b 1 = 2 1 1 1 ℄ T and b 2 = 2 3 1 1 ℄ T

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