Wvecmat10 - ECE 421 Sum 2010 Detailed Solutions Set 10...

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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 2 2 1 3 1 1 1 1 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 2 3 1 1 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 2 2 1 3 1 1 1 1 7 7 7 15 c (c) Compute B B T . Using the definition of the matrix B as defined in equation a we have B B T 2 2 1 3 1 1 1 1 2 1 1 1 2 3 1 1 8 8 4 0 8 10 4 2 4 4 2 0 0 2 0 2 d
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ECE 421 - Sum 2010 Detailed Solutions - Set 10: Vectors and Matrices 2 10-2. Let a matrix A be given by A 7 3 4 1 Compute the following: (a) A 1 , (b) A T A , (c) A 1 A . DETAILED SOLUTION: (a) Compute A 1 . To compute the matrix in part (a), use equation (5b) from the Notes. For the matrix elements in
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