exam2 - x 1 (0) = 1 , x 2 (0) = 0? Determine what the type...

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Exam 2: MAP 4403 * December 1, 2004 Name : Student ID : Provide all details of your work; no details no credit. 1. What is the potential between the cylinders | z | = 1 having potential 100 Volts and | z - i/ 3 | = 0 . 5 having potntial 0 Volts? 2. Is the set of (real) vectors S = { ( x 1 x 2 ) | x 1 x 2 = 0 } a vector space? 3. Determine the rank of the following matrix: 0 0 - 6 - 3 0 1 2 1 0 - 1 1 0 1 1 3 1 1 4 2 1 Determine a basis for the row space of A and a basis for the column space of A . 4. What is the general form of the solution of the system: ˙ x = µ - 1 - 1 - 3 2 x ? What is the solution corresponding to the initial condition
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Unformatted text preview: x 1 (0) = 1 , x 2 (0) = 0? Determine what the type of the equilibrium point at the origin is and discuss stability. 5. Using the method of variation of parameters, Fnd the solution of the system: x = -1-3 2 x + 2 e-t 3 e-3 t DUE DATE: In our classroom at the beginning of class (that is before 9 : 35 am) on Monday December 6. Late exams will not be graded. * Instructor: Patrick De Leenheer. 1...
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