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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456e193f-2af7-4cbe-b4f0-ceb3dbbc38b3%2F7f6cb92d-894c-4d07-ae2e-7e68e2486d15%2Fkh3d36e_processed.png&w=3840&q=75)
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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