* Let be the vector space of all polynomials of degree 2 or less, and let H be the subspace anned by 14x² + 11x + 8, 2x² + 2x + 1 and 6x² + 3x + 4. a. The dimension of the subspace H is 3 b. Is {14x² + 11x + 8,2x² + 2x + 1,6x² + 3x +4} a basis for ? basis for P_2 Be sure you can explain and justify your answer. Enter c. A basis for the subspace H is { 14xx+11x+8, 2xx+2x+1, 6xx+3x+4 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 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4.
a. The dimension of the subspace H is 3
b. Is {14x² + 11x + 8,2x² + 2x + 1,6x² + 3x +4} a basis for ? basis for P_2
Be sure you can explain and justify your answer.
c. A basis for the subspace His { 14xx+11x+8, 2xx+2x+1, 6xx+3x+4
}. 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 14x² + 11x +8, 2x² + 2x + 1 and 6x² + 3x + 4. a. The dimension of the subspace H is 3 b. Is {14x² + 11x + 8,2x² + 2x + 1,6x² + 3x +4} a basis for ? basis for P_2 Be sure you can explain and justify your answer. c. A basis for the subspace His { 14xx+11x+8, 2xx+2x+1, 6xx+3x+4 }. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of x².
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