1. Determine whether the following polynomials: u, v, w in P(t) are linearly dependent or independent: i. u = t³ - 4t² + 3t + 3, ii. u= t³ - 5t² - 2t + 3, v = t³ + 2t² + 4t - 1, v = t³4t² - 3t + 4, w = 2t³t² - 3t + 5; w = 2t³ 17t² - 7t + 9. 2. Write the polynomial f(t) = at² + bt + c as a linear combination of the polynomials: P₁ = (t = 1)², P2 = t - 1, P3 = 1. [Thus, P₁, P2, P3 span the space p₂ (t) of polynomials of degree ≤2]

1. Determine whether the following polynomials: u, v, w in P(t) are linearly dependent or independent: i. u = t³ - 4t² + 3t + 3, ii. u= t³ - 5t² - 2t + 3, v = t³ + 2t² + 4t - 1, v = t³4t² - 3t + 4, w = 2t³t² - 3t + 5; w = 2t³ 17t² - 7t + 9. 2. Write the polynomial f(t) = at² + bt + c as a linear combination of the polynomials: P₁ = (t = 1)², P2 = t - 1, P3 = 1. [Thus, P₁, P2, P3 span the space p₂ (t) of polynomials of degree ≤2]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

See similar textbooks