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# ELEM DIFF EQ & LIN A MATH 2090

LSU

GPA 3.72

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This 23 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 Staff in Fall. Since its upload, it has received 53 views. For similar materials see /class/222637/math-2090-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15

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s 1 p1 Dcwrrmnethcvalueaf hmthatLhemaLnx 1s the awed mamx of a cannxmql linear sysma 475 715202 1s 1 pl Damn the value of a Such 39hal 11 mamx 1s anamx afahnwsy mmthxr m dy many wlnham 3 75 R 5 h 15 1 i 1 pl Solved xyxwm 57117712 Bx 73711 35 M a a 7 a a VA 5 x1p11m7 1 75 0 0 1 aa1a1 9 1 pt HA and B are 3 x 3 matrices det A 3 det B 77 then det AB 7 detB 1 7 det B3 7 3 9 21 10 1ptLetv1 2 122 7 andy 16 3 11 h For What value of h is y in the plane spanned by v1 and 122 11 1 pt Express the vector v J 41 11 4 1 nationofxJ 3 J andyJ 4 J v7x7y 12 1 pt The vectors 1 6 J as a linear combi 14 v1 3 122 4 andvg O O 2 k form a basis for R3 if and only if k y 7 13 1 pt Find a basis of the subspace of R3 de ned by the equation 8x1 7 3x 7 X3 7 7 14 1 pt Find an orthonormal basis of the plane x1 7 8x 7 X3 15 1 pt Find a 2 X 2 matrix A such that O 1 5 and o are eigenvectors of A With eigenvalues 10 and 72 respectively A l Generated by the WeB MK Team J 9 2 8 1 has one eigenvalue of multiplicity 2 Find this eigenvalue and the dimenstion of the eigenspace eigenvalue 2 7 dimension of the eigenspace 7 Is the matrix A defective Type yes or no 7 16 1 pt The matrix A 17 1 pt Find the eigenvalues and associated unit eigenvec tors of the symmetric matrix smaller eigenvalue 2 7 associated unit eigenvector J J larger eigenvalue 2 7 associated unit eigenvector J The above eigenvectors form an orthonormal eigenbasis for A 18 1 pt Find y as a function ofx if y 7 12 07 W 5 0 3 0 4 W 19 1 pt Find y as a function ofx if ym713y 36y 12011 W 23 M0147 MO 21 yx 7 20 1 pt Solve the system dx 7 8 4 E 12 6 x with the initial value x0 J 2 J xt J V4 o quotIZVXL io4z15f D H bale L wo Y F12 w ngL Q C LCMVFZ39VWJ 1 CB Co 539lrkl 5 J SDW Q Q a New 39qJr IC L7OJLUJ Pr Olol Frill I I yl Lx bvl D Lgt 39 1 0 v 717 72 quotKv l E D M09 u 07104 0 h J 0 9quot177 2 39 E MD 941212j2u13 fr 04510341 gt57 mt L y CELkLLJ z r 3 9144 g o r 7 x L4 V J Q 39 O 1 D yLHD L J Cf E gt 5 LU 6130 4 L Ema lr t ZD 24 739 rl Ogt Colt 4 Czsm 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correct answer or to alert you if you are making some kind of mistake Usually you can attempt a problem as many times as you want before the due date However if you are having trouble guring out your error you should consult the book or ask a fellow student or your professor for help Don t spend a lot of time guessing 7 it s not very ef cient or effective Give 4 or 5 signi cant digits for oating point numerical answers For most problems when entering numerical answers you can if you wish enter elementary expressions such as 2 3 instead of 8 sin3 pi2instead of 1 e ln2 instead of 2 2 tan3 4 7 sin5 6 7 78 instead of 276203413 etc Here s the list of the functions which WeBWorK understands You can use the Feedback button on each problem page to send email to the professor 1 1 pt Given the matrix A 8 j J nd its determi nant The determinant of A is 2 1 pt If 7 72i 72i A 7 i O 74i i nd Al 7 1 O 2 3 1 pt Given the matrix 0 2 3 1 O 1 a nd its determinant Your answer is 7 b does the matrix have an inverse Your answer is input Yes or N o 7 1 O O 41ptIfA O 1 O O k 1 then det A 7 O 1 O 51ptIfA 1 O O O O 1 then det A 7 3 O O O 6 5 O O 61pt1fA 5 77 5 0 6 2 2 6 then det A 7 6 5 2 1 6 O 5 5 5 3 71ptIfA O O 2 8 1 O O O 8 7 O O O O 5 then det A 7 8 2 pts Suppose that a 4 X 4 matrix A with rows v1 122 13 and V4 has determinant detA 76 Find the following determi nants V1 det 212 V3 2V4 V4 9 3 pts If A and B are 2 X 2 matrices det A 75 det B 8 then det AB 7 det 3A detAT detB 1 detB3 7 a b c 10 2 pts Given det d e f 2 nd the following g h i determinants det d e f 7 7 8g 8h 8i 7 a b c det 9d 9e 9f 7 7 g h i 7 a b c det g h i 7 7 d e f 11 1 pt Find k such that the following matrix M is singular 3 1 3 12k k 7 33 6O 1 4 121ptlfA3 I ThenA 1i 1 1 1 131ptlfA 0 1 4 0 0 1 ThenA l 7 7 12 31 14 lptlfA 3 10 26 3 8 Then A 1 Generated by the WeB MK Team 15 1 pt Consider the following two systems 3x743 73 72x3y 1 b 3x743 2 72x3y 3 i Find the inverse of the common coef cient matrix of the two systems ii Find the solutions to the two systems by using the inverse ie by evaluating A713 where B represents the right hand side ie B 713 for system a and B for system 03 3 Solution to system a x y Solution to system b x 7 y

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