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(a) Let A = {₁,...Un} be a basis for a finite dimensional real vector space V. Define the corresponding dual basis A* for the dual space V* (b) Let A = {(2, 1), (3,4)} be a basis for R2, what is the dual basis A*?

(a) Let A = {₁,...Un} be a basis for a finite dimensional real vector space V. Define the corresponding dual basis A* for the dual space V* (b) Let A = {(2, 1), (3,4)} be a basis for R2, what is the dual basis A*?

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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(a) Let A = {₁,...Un} be a basis for a finite dimensional real vector space V. Define the corresponding dual basis A* for the dual space V* = {(2, 1), (3, 4)} be a basis for R2, what is the dual basis A*? (b) Let A = (c) Let I: R² → R be defined by I'((x₁, x2)) = 8x₁ - 7x2. Express I in terms of the dual basis in part (b).
Transcribed Image Text:(a) Let A = {₁,...Un} be a basis for a finite dimensional real vector space V. Define the corresponding dual basis A* for the dual space V* = {(2, 1), (3, 4)} be a basis for R2, what is the dual basis A*? (b) Let A = (c) Let I: R² → R be defined by I'((x₁, x2)) = 8x₁ - 7x2. Express I in terms of the dual basis in part (b).
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