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Q1: Recall the definition of 1-1, norm and - norm on R². Consider the matrix A= as a linear map from R² to R². a11 912) azı azz Find a positive constant C₁ >0 such that AxSCx₂ DNE Vx ER². Conclude from here that the linear map A acting from (R²,-₁) into (R².-) is continuous.

Q1: Recall the definition of 1-1, norm and - norm on R². Consider the matrix A= as a linear map from R² to R². a11 912) azı azz Find a positive constant C₁ >0 such that AxSCx₂ DNE Vx ER². Conclude from here that the linear map A acting from (R²,-₁) into (R².-) is continuous.

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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Q1: Recall the definition of 1-1, norm and norm on R². Consider the matrix A= as a linear map from R² to R². /911 ar azı azz Find a positive constant C₂ > 0 such that AxSCx₂ Vx ER². Conclude from here that the linear map A acting from (R².II-₁) into (R².-) is continuous.
Transcribed Image Text:Q1: Recall the definition of 1-1, norm and norm on R². Consider the matrix A= as a linear map from R² to R². /911 ar azı azz Find a positive constant C₂ > 0 such that AxSCx₂ Vx ER². Conclude from here that the linear map A acting from (R².II-₁) into (R².-) is continuous.
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