Estimate the eigen values of the matrix:
using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.
For estimating the eigenvalues of a matrix using Gerschgorin bounds, each eigenvalue lies within at least one of the Gerschgorin discs. Consider a square matrix $A = [a_{ij}]$ of order $n$. The Gerschgorin discs are defined for each row as $D_i = \{z \in ________ ____ _______ __________ ______ __________ _______ __________ _______ _______ _________.
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Using the data sin (0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin (0.15) by Lagrange’s interpolation. Also obtain a bound on the truncation error.
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