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MAT485-2007Fall

MAT485-2007Fall - y"-3y 2y = e t • 8 7(18 pts Use the...

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MAT 485, Fall 2007 NAME: Final Exam 1
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2 1) (18 pts) I)Let ( 3 2) (2 -2) (1 -3 5) A = 20 -1 ,B = 3 4 ' C = 2 -4 6 Find A + B, 2B, AB, and CTB.
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3 2) (18 pts) Solve by the Gauss-Jordan procedure: x + 3y + 2z = 5 2x + 7y 4z = 8 2x + 8y + 3z = 2.
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4 3) (18 pts) A transformation T(v) = Av is given by the matrix A (; -i ~3 ~7). 1 2 3 11 Find the kernel, nullity and rank of T and the general solution of the homogeneous system Ax O.
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5 4) (18 pts) Solve the initial value problem: Y I = ycotx,
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6 5) (18 pts) Solve the initial value problem yl ty = t, y(O) 2.
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7 6) (18 pts) Find the general solution of the differential equation:
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Unformatted text preview: y" -3y' + 2y = e t • 8 7) (18 pts) Use the method of variation of parameters to find the general solution of the differential equations: y" 4y' + 5y = e 2x tan x. 9 8) (18 pts) Use the Laplace transform to solve the initial value problem: yl -Y = 2 step(t - 2), y(O) = 1. 10 9) (18 pts) Solve the initial value problem: I x = (1-1 4 2) x, x(O)=(~). 11 10) (20 pts) Solve the system 12 11) (18 pts) Find all equilibrium points of the given systems and classify their stability and geometry: x' =x2 + y y' =X _ y2...
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MAT485-2007Fall - y"-3y 2y = e t • 8 7(18 pts Use the...

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