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Let 1+ €² A ^= [+²² 142] + where , & € R are free parameters. and (a) Compute ₂ (A) = ||A||2||A¹||2. What happens to the condition number ₂ (A) when € → 0? (b) Compute R(A) and N(A), when € 0. What about € = 0? (c) For € 0, solve Ax = b using the formula (Cramer's rule) A-1 b = [2²6]. 2-8 1 [ det A-021 a11 How does a behave, when 8 = 0 and → 0? What about 80 and € → 0? a22

Let 1+ €² A ^= [+²² 142] + where , & € R are free parameters. and (a) Compute ₂ (A) = ||A||2||A¹||2. What happens to the condition number ₂ (A) when € → 0? (b) Compute R(A) and N(A), when € 0. What about € = 0? (c) For € 0, solve Ax = b using the formula (Cramer's rule) A-1 b = [2²6]. 2-8 1 [ det A-021 a11 How does a behave, when 8 = 0 and → 0? What about 80 and € → 0? a22

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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4. Let [1+2 where €, 8 € R are free parameters. A || 1 1+ €² and b (a) Compute ₂(A) = ||A||2||A¯¹||2₂. What happens to the condition number £₂(A) when € → 0? (b) Compute R(A) and N(A), when €0. What about € = 0? (c) For € 0, solve Ax = b using the formula (Cramer's rule) A-¹ [2 = 1 -012 det A a11 How does x behave, when 8 = 0 and → 0? What about 80 and € → 0? a22 2 -a21
Transcribed Image Text:4. Let [1+2 where €, 8 € R are free parameters. A || 1 1+ €² and b (a) Compute ₂(A) = ||A||2||A¯¹||2₂. What happens to the condition number £₂(A) when € → 0? (b) Compute R(A) and N(A), when €0. What about € = 0? (c) For € 0, solve Ax = b using the formula (Cramer's rule) A-¹ [2 = 1 -012 det A a11 How does x behave, when 8 = 0 and → 0? What about 80 and € → 0? a22 2 -a21
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