Question

Let A  =  58 9 1 9 20 9 59 9 A has λ  =  7...

Let

A  = 
58
9
1
9
20
9
59
9


A has λ  =  7 as an eigenvalue, with corresponding eigenvector  
1
5
 , and λ  =  6 as an eigenvalue, with corresponding eigenvector  
−1
4
 .  Find the solution to the system
y′1   =  
58
9
 y1  + 
1
9
 y2
y′2   =  
20
9
 y1 +  
59
9
 y2

that satisfies the initial conditions y1(0)  =  0 and  y2(0)  =  3. What is the value of y1(1)
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