3.118 Let B be the standard basis for P3. In each part of this exercise, (i) give B coordinate vectors for each polynomial, (ii) express one of the coordinate vectors as a linear combination of the others, (iii) express one of the given polynomials as a linear combination of the others, and (iv) find a basis for the span of the set of polynomials. (a) {10x+14x², 1 + 2x + 3x², 2 + 14x + 20x²}

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
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3.118 Let B be the standard basis for P3. In each part of this exercise, (i) give B
coordinate vectors for each polynomial, (ii) express one of the coordinate
vectors as a linear combination of the others, (iii) express one of the given
polynomials as a linear combination of the others, and (iv) find a basis for
the span of the set of polynomials.
(a) {10x+14x², 1 + 2x + 3x², 2 + 14x + 20x²}
(b) ✔✔ {1−4x + 4x² + 4x³, 2 − x + 2x² + x³, −17 − 2x − 8x² + 2x³ }
{1+2x+3x³, 2 + x + x² + x³, 1+ 4x + 3x² − 3x³, 3 + 15x + 8x² −
4x³,3 – 11x – 9x² + 18x³}
3
(c)
Transcribed Image Text:3.118 Let B be the standard basis for P3. In each part of this exercise, (i) give B coordinate vectors for each polynomial, (ii) express one of the coordinate vectors as a linear combination of the others, (iii) express one of the given polynomials as a linear combination of the others, and (iv) find a basis for the span of the set of polynomials. (a) {10x+14x², 1 + 2x + 3x², 2 + 14x + 20x²} (b) ✔✔ {1−4x + 4x² + 4x³, 2 − x + 2x² + x³, −17 − 2x − 8x² + 2x³ } {1+2x+3x³, 2 + x + x² + x³, 1+ 4x + 3x² − 3x³, 3 + 15x + 8x² − 4x³,3 – 11x – 9x² + 18x³} 3 (c)
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