Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4. a. The dimension of the subspace H is b. Is {14x² + 11x +8,2x² + 2x + 1,6x² + 3x +4} a basis for ? choose Be sure you can explain and justify your answer. c. A basis for the subspace H is { }. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of x².
Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4. a. The dimension of the subspace H is b. Is {14x² + 11x +8,2x² + 2x + 1,6x² + 3x +4} a basis for ? choose Be sure you can explain and justify your answer. c. A basis for the subspace H is { }. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of x².
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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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 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4.
a. The dimension of the subspace H is
b. Is {14x² + 11x + 8,2x² + 2x + 1,6x² + 3x +4} a basis for ₂? choose
Be sure you can explain and justify your answer.
c. A basis for the subspace H is {
}. Enter
a polynomial or a comma separated list of polynomials, where you can enter xx in place of x².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8c5cbec-f2bb-49b4-94bb-4d6293937097%2F8f3624d8-beef-4b31-8533-b7a7226524b5%2Fgarz9ak_processed.png&w=3840&q=75)
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 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4.
a. The dimension of the subspace H is
b. Is {14x² + 11x + 8,2x² + 2x + 1,6x² + 3x +4} a basis for ₂? choose
Be sure you can explain and justify your answer.
c. A basis for the subspace H is {
}. Enter
a polynomial or a comma separated list of polynomials, where you can enter xx in place of x².
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