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# ELEM DIFF EQ & LIN A MATH 2090

LSU

GPA 3.72

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This 3 page Class Notes was uploaded by Madison Gottlieb Sr. on Tuesday October 13, 2015. The Class Notes belongs to MATH 2090 at Louisiana State University taught by J. Morales in Fall. Since its upload, it has received 35 views. For similar materials see /class/222626/math-2090-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15

MATH 2090 PRACT1CE PROBLEMS FOR TEST 1 SEPTEMBER 2011 Use short precise and complete English sentences to explain your an swers Supply enough words so that the steps in your reasoning can be easily followed Credit may will be withdrawn from answers that are not properly and clearly explained Please note that no books notes or cal culators are permitted for tests 1 Verify that yx 0 and yx x6 are both solutions of the initial value problem d y 6xy23 y0 0 dx Explain why the Existence and Uniqueness Theorem does not ap ply in this case 2 Solve the initial value problem dyZt 0 1 dx yanx y 3 Find the general solution of the differential equation dy1 2 dx xyx2139 4 Solve the differential equation 2x2 x y y 3 5 Solve the initial value problem 4 9 1 0 y xy x3 y 6 Find the general solution of the differential equation dy xy xz2y2 dx 2x y 7 Solve the initial value problem x4yy392x y y1 1 8 Find the general solution of the Bernoulli differential equation I 1 3 y Etanxy 2y s1nx 9 Show that the differential equation 2xy 1dx xzdy 0 is exact and nd its general solution 10 Solve the initial value problem ny x2 d d 0 1 1 x1 x x1 y y Hint Find an integrating factor to make the equation exact 1 1 2 0 11 j 11 LetA 2 0 2 2 andB 0 1 FindAB 1 2 1 1 0 12 Let A 2 f2 Find all values of a and b for which A2 A 13 Reduce the matrix below to reduced row echelon form and deter mine its rank 1 2 2 6 1 2 4 1 3 0 2 4 3 9 1 39 1 2 0 0 0 14 Solve the following system oflinear equations x1x22x3 2 xl x2x3 2 1 4x1 2x25X3 1 15 Solve the system oflinear equations 3x25X3ZX4 5 x2 2X3 X4 2 x1 9xz 13xg 4X4 14 2x1 3x2 X32x4 3 using GaussJordan elimination ie putting the associated aug mented matrix in reduced rowechelon form 16 Determine the value of h such that the matrix below is the aug mented matrix of a consistent linear system of equations OJNH C JgtIJ 0 1 1 4 2 h 17 Calculate the inverse of the following matrices if it exists 1 2 3 1 2 1 a A 2 5 9 b B 2 5 1 3 7 11 3 7 2 18 A n x 71 matrix A is called orthogonal if A 1 2 AT Show that the matrix cosH sinH sinH cosH is orthogonal 19 Compute the signature ofthe permutation 2 16 54 3 1 5 2 3 1 7 3 1 20 Let A 2 1 0 1 Compute detA Is A nonsingular 4 11 5 5 Justify your answer

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