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3. Suppose V = {r²,r, 1} and U = {3x²,2-1,4} are two ordered bases for P₂. That is, in the notation of the book, = 2²,0₂ 1,03 = 1 and u₁ = 32²,u₂ = 2-1, uz = 4. (a) Find the transition matrix corresponding to the change of basis from V to U. (b) Use the transition matrix to find the coordinate vector of x = 5r²-3r+4 with respect to U. That is, find (x)₁/

3. Suppose V = {r²,r, 1} and U = {3x²,2-1,4} are two ordered bases for P₂. That is, in the notation of the book, = 2²,0₂ 1,03 = 1 and u₁ = 32²,u₂ = 2-1, uz = 4. (a) Find the transition matrix corresponding to the change of basis from V to U. (b) Use the transition matrix to find the coordinate vector of x = 5r²-3r+4 with respect to U. That is, find (x)₁/

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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3. Suppose V = {x²,r, 1} and U = {3r²,2-1,4} are two ordered bases for P₂. That is, in the notation of the book, ₁ = 2²,0₂ = 2,03= 1 and u₁ = 32²,u₂ = 2-1, uz = 4. (a) Find the transition matrix corresponding to the change of basis from V to U. (b) Use the transition matrix to find the coordinate vector of x = That is, find (x)U 5x²-3x+4 with respect to U.
Transcribed Image Text:3. Suppose V = {x²,r, 1} and U = {3r²,2-1,4} are two ordered bases for P₂. That is, in the notation of the book, ₁ = 2²,0₂ = 2,03= 1 and u₁ = 32²,u₂ = 2-1, uz = 4. (a) Find the transition matrix corresponding to the change of basis from V to U. (b) Use the transition matrix to find the coordinate vector of x = That is, find (x)U 5x²-3x+4 with respect to U.
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