12. B' = (1 + x − 2x², 3+2x + x² − 2x³,2+x+3x² − 2x³). -
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 37EQ
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In exercises 8 - 12 decide if the sequence B' is a basis for the space S of exercise 7.
See Method (5.3.2). Note that if there are the right number of
show that the vectors belong to the subspace S.
#12 please and thank you -- also will vote up
![7. Let S = {ao + a₁x + a₂x² + a3x³ € R3 [x] : a₁ + a₁ + a2 + 3a3 = 0}. Verify that
B= (-1 + x,-1+x²,−3+x³) is a basis of S.
In exercises 8 - 12 decide if the sequence B' is a basis for the space S of exercise 7.
See Method (5.3.2). Note that if there are the right number of vectors you still have to
show that the vectors belong to the subspace S.
8. B' = (1 + x + x² − x³,1 + 2x − x³, x + 2x² − x³).
-
9. B' = (3 – x³, 3x – x³, 3x² – x³).
10. B' = (1 + 2x + 3x² − 2x³,2+3x+ x² − 2x³).
11. B' = (1 + x − 2x², −2+x+x²,1 − 2x + x²,1 + x + x² − x³).
-
12. B' = (1 + x2x², 3+2x+x²–2x³, 2+x+3x² − 2x³).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F293032ce-89a7-4d5a-8a29-aae96cb1d151%2F2efea50c-6d9d-42d9-b538-b51cc238ecdf%2Fk7mvuwn_processed.png&w=3840&q=75)
Transcribed Image Text:7. Let S = {ao + a₁x + a₂x² + a3x³ € R3 [x] : a₁ + a₁ + a2 + 3a3 = 0}. Verify that
B= (-1 + x,-1+x²,−3+x³) is a basis of S.
In exercises 8 - 12 decide if the sequence B' is a basis for the space S of exercise 7.
See Method (5.3.2). Note that if there are the right number of vectors you still have to
show that the vectors belong to the subspace S.
8. B' = (1 + x + x² − x³,1 + 2x − x³, x + 2x² − x³).
-
9. B' = (3 – x³, 3x – x³, 3x² – x³).
10. B' = (1 + 2x + 3x² − 2x³,2+3x+ x² − 2x³).
11. B' = (1 + x − 2x², −2+x+x²,1 − 2x + x²,1 + x + x² − x³).
-
12. B' = (1 + x2x², 3+2x+x²–2x³, 2+x+3x² − 2x³).
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