Science:Math Exam Resources/Courses/MATH307/December 2005/Question 06 (b)
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Question 06 (b) 

Consider the differential equation (b) Find the matrix exponential when 
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Hint 

Science:Math Exam Resources/Courses/MATH307/December 2005/Question 06 (b)/Hint 1 
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Solution 

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Find the eigenpairs to diagonalize the matrix!
Setting the above to zero and solving yields
Let Find corresponding eigenvectors
From the second row: –> corresponding eigenvector
From the second row: –> corresponding eigenvector
So
NOTE: please ignore the <span>, <>.. not sure how to get rid of them. 