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1.F.2 Let B = {1, x, x², x³} be the standard basis of P<3. a) What are the coordinates of 5³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – r³, x + 2x³, 1+ x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(x–1)³, (x- 2)², (x – 3)(x² – 8x +11)}.

1.F.2 Let B = {1, x, x², x³} be the standard basis of P<3. a) What are the coordinates of 5³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – r³, x + 2x³, 1+ x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(x–1)³, (x- 2)², (x – 3)(x² – 8x +11)}.

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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1.F.2 Let B = {1, r, x², x³} be the standard basis of P<3. a) What are the coordinates of 52³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, 2³ comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – 23, r + 2a°, 1 + x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(r-1)³, (x– 2)2, (x – 3)(x² – 8x + 11)}.
Transcribed Image Text:1.F.2 Let B = {1, r, x², x³} be the standard basis of P<3. a) What are the coordinates of 52³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, 2³ comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – 23, r + 2a°, 1 + x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(r-1)³, (x– 2)2, (x – 3)(x² – 8x + 11)}.
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