MAT485-2004Spring

# MAT485-2004Spring - Mat 485 Final Exam Apr. 30, 2004...

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Unformatted text preview: Mat 485 Final Exam Apr. 30, 2004 Directions: Answer all questions in your bluebook. Include supporting work as necessary. Unsupported work may receive little or no partial credit. Please write neatly. Start each problem on a new page of the bluebook. If you use more than one bluebook, make sure your name is on all of them. When ﬁnished, place test sheet inside the bluebook. 3 2 6 l l.[12 pts] Let A=[2 2], B=[O 3].Find A+B, 2A, and AB. 1 0 3 2 2.[10 pts] The RREF for a particular system of linear equations is O l — 4 5 . 0 0 0 0 Describe the general solution to the system of equations 3.[12 pts] Solve y” + 6 y’ + 9y = Br using the method of undetermined coefﬁcients. 4.[15 pts] Solve the system of linear homogeneous differential equations 16’ = x + y y' = 4x — 2y 5.[12 pts] Find the inverse Laplace transform for the function F (s) = 2—3S—. s —s—6 6.[15 pts] Solve the IVP y” + 2y’ + 2y = 0, y(0) = 0, y’(0) =1 by using the Laplace transform. 7.[l4 pts] Use separation of variables to solve the ﬁrst order equation Q _ (yz +l)-sin(x) dx y 8.[10 pts] Consider the linear transformation T : R3 -—) R2 given by T(x,y, 2) = (2, y ex) . . . . , 3 . 2 ( a) Find the matrix for T usmg the standard ba51s for R and the standard ba51s for R ( b ) Find a basis vector for the kernel of T. 1,” :Eal 3mm; t) SinMat) e" sin(bt) ‘ if“! ms(bt) 'mmnm bah-t range is>0 Is>0 12625:” is>a gs>0 'S>0 s > {(1% ys>fné gs>a ‘s>a is>a, n a pos. integer ...
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## This note was uploaded on 01/15/2012 for the course MAT 485 taught by Professor Staff during the Fall '11 term at Syracuse.

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MAT485-2004Spring - Mat 485 Final Exam Apr. 30, 2004...

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