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A2 is a 2 x 2 matrix with all 1's as its entries, and A3 is a 3 x 3 matrix with all 1's as its entries, and An is an n x n matrix with all 1's as its entries. Find n linearly independent eigenvectors of An. What are their associated eigenvalues.

I have no idea how to do this. Any help would be super great!

EDIT:

Does v1=[1,0,...0], v2=[1,1,0,...0], vn=[1,1,1,...1] work? This is really hard since the null space of An only has n-1 linearly independent vectors.

I have no idea how to do this. Any help would be super great!

EDIT:

Does v1=[1,0,...0], v2=[1,1,0,...0], vn=[1,1,1,...1] work? This is really hard since the null space of An only has n-1 linearly independent vectors.

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