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# Engineering Mathematics MATH 3321

UH

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This 3 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 3321 at University of Houston taught by Jeffrey Morgan in Fall. Since its upload, it has received 48 views. For similar materials see /class/208395/math-3321-university-of-houston in Mathmatics at University of Houston.

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Date Created: 09/19/15

N 1quot 4 V39 0 1 9 50 Math 3321 Onljne Review Problems Solve u t2u I 6quot 110 1 Give the general solution to xyz x 1 1 4 Use elementary row operations to find the inverse of the matrix 1 2 1 3 7 1 x 4y 32 1 Use elementary row operations to solve the system x 3 y z 2 x 3y 22 1 1 0 1 The matrix A is 3 by 3 and A 1 0 l 2 Solve the system of equations 1 1 0 x 1 given by A y 1 z 2 1 0 1 Give the determinant of l 1 1 by expanding across row 1 210 Use Laplace transforms to nd the solution to uquott utexp2t u01 u3900 1 36 Find the function whose Laplace transform is 2 s 3 s 4 s 7 4 The eigenvalues of 12 7 are 1 and 1 The eigenvectors associated with 1 are 2 nonzero scalar mult1ples 0f 3 and the e1genvect0rs ass0c1ated w1th 1 are 1 nonzero scalar multiples of Solve the initial value problem x 7x 4y y39l2x 7ye x0 1y01 x2ky3 kx3yl O Determine the values of k for which the system J is inconsistent Give the form ofa particular solution to y t 3y t 4yt sin t 2equot N Solve uquott 3u t2uteXp t u0l u390 0 LA Use Euler s method With a step size of 01 to approximate y02 where y solves y39 x2y y0 0 14 Use Improved Euler s method with a step size of 01 to approximate yO l where ysolves y39 x2y y0 0 15 Suppose A l 2 l Give the characteristic polynomial of A l Give all of the eigenvectors associated with the 2 2 3 16 Suppose A l 2 1 Verify that the eigenvalues ofA are l 4 and 2 Suppose A l 2 I eigenvalue 4 x 4y 2 1 18 Give a value of c so that the system 2x 7y 22 2 has at least one solution x 3y zc O N O N 4 N UI N O N 1 Show that the vectors 1 2 5 7 Let A 12 l l 2 are linearly dependent l 2 Explain why a linear system of 2 equations with 2 unknown either has 0 l or in nitely many solutions x397x 4y y39l2x 7ye 4 Give em and then use 6 to solve 7 x0 1y01 Find and classify the steady states of the differential equation u u l u2 Give the values of the parameter a so that the steady state 0 of u 39 au u3 is asymptotically stable v 2 2 Find and classify the steady states of the system u V M v u v Rework all of the problems from the midterm exam Rework all of the problems from the written homework and online quizzes Study the examples worked in the online sessions Note You can bring a Laplace transform formula sheet to the nal exam

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