Let Gaussian elimination without pivoting be applied to a symmetric positive definite matrix A, Write A, the matrix obtained after the first step, as an (1) a) Show that B b) If a ≤1, then b ≤1. = a₁1 a 12 0 B (n-1)(n-1) B(n-1)(n-1) = (b) is symmetric and positive definite.

Let Gaussian elimination without pivoting be applied to a symmetric positive definite matrix A, Write A, the matrix obtained after the first step, as an (1) a) Show that B b) If a ≤1, then b ≤1. = a₁1 a 12 0 B (n-1)(n-1) B(n-1)(n-1) = (b) is symmetric and positive definite.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Matrices And Determinants

Section: Chapter Questions

Problem 11CC

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Question

. Let Gaussian elimination without pivoting be applied to a symmetric positive definite
matrix A, Write A, the matrix obtained after the first step, as
an
a) Show that B
(n-1)(n-1)
A(¹)
b) If a ≤1, then b ≤1.
=
a₁1 a12
0
B
(n-1)(n-1)
= (b) is symmetric and positive definite.

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