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leamontanotechu.ca/courses/6933/assignments:/44802 = 10046.202005XLIST Assignments Assignment 4 - Due Friday July 31 before 3

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

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Answer #1

Given linear system of equations y,=84, -loy, y₂=59,-79, 1 ) Y = Ay. ya y, y= 8 -10 wetficient matrix, A= ( [5:-) find eigeeigen 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 corresponding5x, - 10% - [:] 5x - Lola elements compare corresponding sx, -100=0. 2,= 2X2 X₂= 21, [x] x --[i, 1.), eigen vector, v. 2) solput x=0 solution 3(0) 4,10) e YLO) - <1)>=--(3) (31-193-] (3) = [ Ct +262 citci comparing corresponding elements. C, +262 = -

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