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# hw08 - ENEE 241 01 HOMEWORK ASSIGNMENT 8 Due Tue 03/10...

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ENEE 241 01* HOMEWORK ASSIGNMENT 8 Due Tue 03/10 Solve by hand without using calculator matrix functions. Show all intermediate steps. Problem 8A Consider the following three matrices: A = 1 - 3 - 2 1 - 2 6 - 3 - 1 3 2 2 - 1 - 1 4 3 2 B = 1 - 4 2 - 3 - 2 3 1 7 1 - 1 1 - 1 - 1 - 1 3 4 C = 2 - 1 1 - 2 4 - 2 1 - 3 1 - 2 3 1 1 1 - 3 - 2 (i) (12 pts.) Determine whether each matrix is nonsingular or singular. (ii) (2 pts.) Determine all solutions of the equation Ax = 0 . (iii) (2 pts.) Compute the product Bx (1) , where x (1) = £ 12 - 11 - 13 10 / T . In what way is the result consistent with the answer to part (i)? (iv) (4 pts.) Does there exist x such that Cx = d , where d = £ 0 1 - 4 5 / T ? If such x exists, is it unique? ( Hint: Include d alongside with C in the forward elimination phase. ) Problem 8B Consider the three-dimensional vectors v = [2 6 1] T and w = [8 - 3 2] T . (i) (3 pts.)

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hw08 - ENEE 241 01 HOMEWORK ASSIGNMENT 8 Due Tue 03/10...

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