Quiz 3 (4-20-2009) solutions

without actually solving the equation please show

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Unformatted text preview: equation, please show that Proof. By definition The first and the second determinants are zero because they have identical rows. Thus, Because y , y , y are solutions of the homogeneous portion of the equation, we have 1 2 3 1 2 3 1 2 3 Therefore 1 2 3 1 2 3 1 1 Multiplying Row-1 by 1 2 2 and Row-2 by 2 3 3 and add them to Row-3, we have 1 1 1 1 Thus, 1 Q3-3 (7.5 Points): Use Substitution Method and Operator Method to solve the following system of equations (3.75 Points for each method): 2 3 2 Solution: 3 3 (1) Substitution Method. With 2 The characteristic equation is 3 We have 2 , we have 2 3 4 0. 1 2 2 1, 4 . 4 3 2 4 3 2 (2) Operator Method. We have 1 2 0 1 . We use 2 1 3 2 0 2 3 4 0. The characteristic equation is 3 4 0. 1, 4. We have . 2 2, and we have and Therefore, we have the same solutions as found earlier 3 2 4...
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