(Solution) - Show that the m 1 by m 1 -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Pages: 5 Words: 1375

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Show that the (m ? 1) by (m ? 1) tridiagonal method matrix A given by

Show that the (m ? 1) by (m ? 1)
where ? > 0, is positive definite and diagonally dominant and has eigenvalues
Show that the (m ? 1) by (m ? 1)
with corresponding eigenvectors v(i), where v(i)j = sin(ij?/m).