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leamontanotechu.ca/courses/6933/assignments:/44802 = 10046.202005XLIST Assignments Assignment 4 - Due Friday July 31 before 3pm Spring 2030 Assignment 4 - Due Friday July 31 before 3pm Submit Assignment Home Announcements Due Friday by 3pm Points 6 Submitting a file upload File Types pdf Available Jul 23 at 7pm - Jul 31 at 8pm 8 days Assignments Discussions Grades People The purpose of this assignment is for you to develop some familiarity with an application of linear algebra through individual study. The nle submission MUST be a pdf. YOU MAY BE TESTED ON THIS MATERIAL ON THE FINAL EXAM. Please note that no marks will be given on the final answers alone: SHOW YOUR WORK!!! Read through the Differential Equation section Section 5.4 in our Textbook's 12th edition (Section 5.4 in 11th edition). Question: Consider the linear system of differential equations V 81 102 бу Pages Files Syllabus מ7 Y Quizzes Modules 1. (2 marks) Find the eigenvalues of the coefhcient matrix and corresponding eigenvectors 2. (2 marks) Solve the system 3.2 marks) Find the solution that satisfies the initial value conditions (0) = -1, 7(0) = 3 ces р Conferences Collaborations Google Drive My Media Media Gallery Proctortrack.CA Type here to search o G Ü *

Hi, I require assistance please.

Question: Consider the linear system of differential equations
y'1 = 8y1 - 10y2
y'2 = 5y1 -7y2

1. Find the eigenvalues of the coefficient matrix and corresponding eigenvectors.

2. Solve the system.

3. Find the solution that satisfies the initial condition y1(0) = -1, y2(0) = 3

Thank you

Answer 1

Given linear system of equations y,'=84, -loy, y₂=59,-79, 1 ) Y = Ay. y'a y, y= 8 -10 wetficient matrix, A= ( [5:-) find eigen values. la-tal=0 8- c 5 -7-1 7 (8-1) (-7-1) +50=0 .-56_84+74+1²+50=0 x-1-6= ť-3x+28-620 &(4-3) +2(1-3) = (+2) (1-3) = 0 , 34 -2,3

eigen vectors Finding AX= 1x. (A-1)x=0 X = [ 2 ] i) 1 = -2 10 1 [*]= [8] 5 5 4 lon, -1012 = 1] SH, -50r compare corresponding corresponding elements o 107, - 2002 x = x2g 2, X 2, 1 2:1-6 a eigen - 11 (for d= -2), :) A-3 5 -10 21, ما ما ](%) lo 5 -10

5x, - 10% - [:] 5x - Lola elements compare corresponding sx, -100=0. 2,= 2X2 X₂= 21, [x] x --[i, 1.), eigen vector, v. 2) solution of systems of differential equation is da ? Y(x)= Civiela + C₂ V₂ 32 y(«) -2x e + C2 V. [] y, -2X e C 1 : ] t «[?]es Y 3) initial conditions are 5 y, (0) = -1 Yg (0) = 3.

put x=0 solution 3(0) 4,10) e YLO) - <1)>=--(3) (31-193-] (3) = [ Ct +262 citci comparing corresponding elements. C, +262 = - 1 0 Ct Cr (-) E's (2=-4 2 in (+2.1-4)=-), c =-1+8=7g solutions y, = 1)* + (-2)[7)*** y