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Linear Algebra 4

Linear Algebra 4 - ECE 531 LINEAR SYSTEM THEORY Take-home...

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ECE 531 LINEAR SYSTEM THEORY SPRING 2006 Take-home Examination #1 Due: Monday, 13 March 2006 at 11:00am This is a take-home exam; open book, open notes. Please list on the exam paper all outside sources (books, notes, etc.) which you consulted in working the problems. You are to work independently , but feel free to contact me should you have any questions. 1. For ˙ x ( t ) = Ax ( t ), we know that x (0) = 1 2 1 implies x ( t ) = 1 2 1 e - 2 t , that x (0) = 1 1 1 implies x ( t ) = 1 1 1 e - 3 t , and that x (0) = 2 0 1 implies x ( t ) = 2 0 1 e - t , What is A ? Indicate whether or not more than one choice of A is possible, and if so provide all possible choices. 2. For ˙ x ( t ) = Ax ( t ), we know that x (0) = 2 1 implies x ( t ) = 2 1 e - 2 t and that x (0) = 3 2 implies x ( t ) = 3 + 2 t 2 + t e - 2 t . What is A ? Indicate whether or not more than one choice of A is possible, and if so provide all possible choices.

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