Assignment #1 Fall 09 Solutions

# Assignment #1 Fall 09 Solutions - SOLUTIONS ODE Asgt 1 Fall...

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SOLUTIONS ODE Asgt 1 Fall 09 If you get the solutions with another method that you understand stick with it For any questions about the Methods applied for Matrix a) ask Steve, for Matrix b) ask Usman Question 1)a) A= 3 1 0 1 5 0 0 0 4 Multiplicity if the EigenValue ? ? = °± − ? = ° − 3 1 0 1 ° − 5 0 0 0 ° − 4 so det = ° − 4 ² ∗ ³ ° − 3 ² ° − 5 ² + 1 ´ = ° − 4 ² 3 So whe one eigenvalue 4 of Multiplicity 3 Dimension of the eigenspace? ? 4= 1 1 0 1 1 0 0 0 0 so we have 2 eigenvectors 1 1 0 and 0 0 1 . So the dimension of the eigenspace is 2. Defective /Non defective ? We can see that dim(Eigenspace)=2 < Mltiplicity =3 so 2<3 so A is a defective matrix

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Basis of each eigenspace °±² ³ = 4 Basis = 1 1 0 , ´ ´ 0 0 1 µ Rank of the Matrix Numbers of linearly indep columns and rows of A So Rank(A) =3 Question 1)b)

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All the formulaes are in your notes or http://www.aerostudents.com/files/differentialEquations/systemsOfFirstOrderLinearEquations.

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## This note was uploaded on 12/01/2010 for the course MATH 263 taught by Professor Sidneytrudeau during the Fall '09 term at McGill.

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Assignment #1 Fall 09 Solutions - SOLUTIONS ODE Asgt 1 Fall...

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