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Consider the following matrix A and it's inverse A-¹, 0 1 0 200 1 1 A = " || B||4,4 = A-¹ = = Let the "entry-wise" 4-norm of a m x n matrix B (or vector) be defined as 1/4 0.5 0 -1 0 m n ΣΣ 16:14 i=1 j=1 0 1 0 1 a) By hand, calculate ||A||4,4. h) By hand calculate the condition number of A using the "entry-wise" 4-norm (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.

Consider the following matrix A and it's inverse A-¹, 0 1 0 200 1 1 A = " || B||4,4 = A-¹ = = Let the "entry-wise" 4-norm of a m x n matrix B (or vector) be defined as 1/4 0.5 0 -1 0 m n ΣΣ 16:14 i=1 j=1 0 1 0 1 a) By hand, calculate ||A||4,4. h) By hand calculate the condition number of A using the "entry-wise" 4-norm (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.

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 A-¹, Го 1 01 A = 200 1 1 2 A-¹ = 1 m n |||B||4,4 = |bj|4 ΣΣ i=1 j=1 1 Let the "entry-wise" 4-norm of a m × n matrix B (or vector) be defined as 1/4 0.5 0 0 1 a) By hand, calculate || A||4,4. b) By hand calculate the condition number of A using the "entry-wise" 4-norm. (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.
Transcribed Image Text:Consider the following matrix A and it's inverse A-¹, Го 1 01 A = 200 1 1 2 A-¹ = 1 m n |||B||4,4 = |bj|4 ΣΣ i=1 j=1 1 Let the "entry-wise" 4-norm of a m × n matrix B (or vector) be defined as 1/4 0.5 0 0 1 a) By hand, calculate || A||4,4. b) By hand calculate the condition number of A using the "entry-wise" 4-norm. (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.
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