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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For an n X n matrix A, to fi nd its inverse we need to solve AX = In for the n X n matrix X. Writing this equation as A [ x1 x2 • · · xn] = [ e1 e2 · · · en], using the matrix-column form of AX, we see that we need to solve n systems of linear equations: Ax1 = e1, Ax2 = e2, ... , AXn = en· Moreover, we can use the factorization A = LU to solve each one of these systems. use th e approach just outlined to fi nd A -1 for th e given matrix
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