HW7 - ME 391 FALL 2007 HW 7(Due Date Oct 31 2007 ^ ^ ^ ^ 1...

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ME 391: FALL 2007 HW 7 (Due Date: Oct. 31, 2007) 1. Given two vectors k j i a ˆ 4 ˆ 3 ˆ 2 + + = , k j i b ˆ 4 ˆ 6 ˆ 4 - - = , compute the following: (a). b a + 2 (b). b a 3 , b a 3 2 × (c). b comp a , a proj b (d). The angle between a and b 2. (a). Given A is an 1 × m column vector, B is an 2 × m matrix, C is an m m × square matrix and D is a m × 1 row vector, which of the following products are not defined? Give reasons. B A T , A C 3 , A DBB T , ( 29 D B A T - , - I C 2 1 C (b). Given = 0 0 1 0 1 0 1 1 2 A , = 1 1 3 3 2 2 B , = 1 1 1 0 0 1 C , prove that ( 29 T T T T A B C ABC = . Show all the steps. 3. For the following systems of linear equations, determine the row echelon form (REF) of the augmented matrix and state the rank of the coefficient matrix. Find all solutions, if they exist. (a). 18
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This note was uploaded on 07/25/2008 for the course ME 391 taught by Professor Blazer-adams during the Fall '08 term at Michigan State University.

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