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Unformatted text preview: = b + 2 ac cos j n + 1 ,j = 1 , 2 ,...,n. (a) Verify this for n = 1 and then for n = 2 by direct calculation. (b) Verify this for n = 4 using MATLABs eig function, with a =-1, b = 2, and c =-1. (c) Verify this for general n but with c = a (symmetric case) by using the fact that the n n matrix of eigenvectors, V , has elements v ij = sin ij n +1 . [Hint: write out a general interior row of A v j = j v j , which involves just three terms (since the matrix is tridiagonal) and use the trigonometric identity sin( ) = sin cos cos sin to replace the two o-diagonal terms (the ones involving a and c ) with multiples of the diagonal term.]...
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This note was uploaded on 11/02/2009 for the course APMA 2102 taught by Professor Keyes during the Spring '08 term at Columbia.
- Spring '08