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3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of coordinate matrix that changes ẞ'-coordinates into B-coordinates. (a) = {x2, x, 1} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (b) = {1, x, x2} and ẞ' = {a2x² + a1x+ao, b2x² + b₁x+b0, C2x² + c₁x + co} (c) ẞ= {2x2-x, 3x² + 1, x2} and B' = {1, x, x2} (d) ẞ = {x2x1,x1, x2 +1} and B' = {x²+x+4,4x² 3x + 2,2x²+3} (e) ẞ = 1 {x2x, x²+1, x- 1} and B' = {5x22x-3, -2x²+5x+5, 2x² - x - 3} (f) B = {2x² - x+1,x2+3x-2, -x² + 2x+1} and B' = {9x9, x² + 21x2, 3x²+5x+2}

3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of coordinate matrix that changes ẞ'-coordinates into B-coordinates. (a) = {x2, x, 1} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (b) = {1, x, x2} and ẞ' = {a2x² + a1x+ao, b2x² + b₁x+b0, C2x² + c₁x + co} (c) ẞ= {2x2-x, 3x² + 1, x2} and B' = {1, x, x2} (d) ẞ = {x2x1,x1, x2 +1} and B' = {x²+x+4,4x² 3x + 2,2x²+3} (e) ẞ = 1 {x2x, x²+1, x- 1} and B' = {5x22x-3, -2x²+5x+5, 2x² - x - 3} (f) B = {2x² - x+1,x2+3x-2, -x² + 2x+1} and B' = {9x9, x² + 21x2, 3x²+5x+2}

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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Section 2.5: Number 3 (f) only!

 

3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of coordinate matrix that changes 3'-coordinates into B-coordinates. (a) = {x2, x, 1} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (b) = {1, x, x2} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (c) B= {2x2 x, 3x² + 1, x2} and ẞ' = {1, x, x2} B' (d) ẞ= {x²-x+1, x+1, x²+1} and B' = {x²+x+4, 4x2 - 3x + 2,2x²+3} (e) ẞ= {x²-x, x² + 1, x 1} and B' = {5x22x-3, -2x² +5x+5, 2x²-x- (f) ẞ= {2x²-x+1, x²+3x-2, -x²+2x+1} and B= B'= {9x9, x² + 21x2, 3x² +5x+2}
Transcribed Image Text:3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of coordinate matrix that changes 3'-coordinates into B-coordinates. (a) = {x2, x, 1} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (b) = {1, x, x2} and 3' = {a2x² + a1x+ao, b2x² + b₁x + bo, c2x² + c₁x + co} (c) B= {2x2 x, 3x² + 1, x2} and ẞ' = {1, x, x2} B' (d) ẞ= {x²-x+1, x+1, x²+1} and B' = {x²+x+4, 4x2 - 3x + 2,2x²+3} (e) ẞ= {x²-x, x² + 1, x 1} and B' = {5x22x-3, -2x² +5x+5, 2x²-x- (f) ẞ= {2x²-x+1, x²+3x-2, -x²+2x+1} and B= B'= {9x9, x² + 21x2, 3x² +5x+2}
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