creating matrices from vectors

If I have 4 vectors (a, b, c, and d) each of length 1000, how do I then create 1000 two by two matrices from these vectors, such that:
 
myMatrix[i] = matrix(c(a[i],b[i],c[i],d[i]),2)
 
Then I'd like to create a single vector containing the largest eigenvalues of each matrix?
 
(Sorry I am quite new to R)
Many thanks,
James
 
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