Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 7x - 2x² + 2, ·(x² + 2x +2) and 3x − x² + 1. 1 a. The dimension of the subspace H is b. Is {7x − 2x² +2,- (x² + 2x +2), 3x − x² +1} a basis for ➡? choose Be sure you can explain and justify your answer. c. A basis for the subspace His { Enter a polynomial or a comma separated list of polynomials (where you can enter xx in place of x²)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace
spanned by 7x - 2x² + 2,
·(x² + 2x +2) and 3x − x² + 1.
1
a. The dimension of the subspace H is
b. Is {7x − 2x² +2,- (x² + 2x +2), 3x − x² +1} a basis for ➡? choose
Be sure you can explain and justify your answer.
c. A basis for the subspace His {
Enter
a polynomial or a comma separated list of polynomials (where you can enter xx in place of x²)
Transcribed Image Text:Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 7x - 2x² + 2, ·(x² + 2x +2) and 3x − x² + 1. 1 a. The dimension of the subspace H is b. Is {7x − 2x² +2,- (x² + 2x +2), 3x − x² +1} a basis for ➡? choose Be sure you can explain and justify your answer. c. A basis for the subspace His { Enter a polynomial or a comma separated list of polynomials (where you can enter xx in place of x²)
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