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Consider the following matrix A and it's inverse A¹, 1/2 -4 -1/2 1/2 By hand, calculate the condition number of A using the infinity norm. A-1 2 1 2 3 1 7 -1 5/2 -3/2 1/2

Consider the following matrix A and it's inverse A¹, 1/2 -4 -1/2 1/2 By hand, calculate the condition number of A using the infinity norm. A-1 2 1 2 3 1 7 -1 5/2 -3/2 1/2

Advanced Engineering Mathematics
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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Consider the following matrix A and it's inverse A¹, 0 1 3 2 1 3 1 1/2 -4 5/2 3 -3/2 -1/2 1/2 -1 1/2 By hand, calculate the condition number of A using the infinity norm. A = 1
Transcribed Image Text:Consider the following matrix A and it's inverse A¹, 0 1 3 2 1 3 1 1/2 -4 5/2 3 -3/2 -1/2 1/2 -1 1/2 By hand, calculate the condition number of A using the infinity norm. A = 1
Expert Solution
Step 1

Given matrix A=013121231 and its inverse A−1=12−452−123−3212−112.

We have to calculate the condition number of A using the infinity norm.

Infinity norm is defined as A∞=max1≤i≤m∑j=1naij. 

A∞=max0+1+3,1+2+1,2+3+1=max4,5,6=6

Hence A∞=6.

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