2. Let Gaussian elimination without pivoting be applied to a symmetric positive definitematrix A, Write Aº, the matrix obtained after the first step, as RecorderanA(¹)a₁1 a 120B(n-1)(n-1)a) Show that B(n-1)(n-1) = (b) is symmetric and positive definite.b) If |a₁|≤1, then |b₁|≤1. 1. Let A = (a)nxn be symmetric and positive definite. Show thata) a>0, i=1,2,...,n.b) |a₁|<(a„ª,„)¾‚, i, j=1,2,…….….,.'ii

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1. Let A=(a)nxn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. b) |a₁|<(a„a,„)³¾, i, j=1,2,...,..

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

2. Let Gaussian elimination without pivoting be applied to a symmetric positive definite
matrix A, Write Aº, the matrix obtained after the first step, as Recorder
an
A(¹)
a₁1 a 12
0
B
(n-1)(n-1)
a) Show that B(n-1)(n-1) = (b) is symmetric and positive definite.
b) If |a₁|≤1, then |b₁|≤1.

1. Let A = (a)nxn be symmetric and positive definite. Show that
a) a>0, i=1,2,...,n.
b) |a₁|<(a„ª,„)¾‚, i, j=1,2,…….….,.
'ii

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