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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 = I_n for the n X n matrix X. Writing this equation as A [ x₁ x₂ • · · x_n] = [ e₁ e₂ · · · e_n], using the matrix-column form of AX, we see that we need to solve n systems of linear equations: Ax₁ = e₁, Ax₂ = e₂, ... , AX_n = e_n· 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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