3 Solved Questions for Exam 2 - Introduction Applied Linear Algebra | MATH 254, Exams of Linear Algebra

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Math 254 — Introduction to Linear Algebra, Instructor: Rakhim Aitbayev, November 1, 2007 Problem 4. 1. Show that the set B = {p,(t) = 1+ 2+, p(t) =1—2¢4+ 42, p(t) =1—-t-# is a basis for the vector space P, of polynomials of degree < 2. thiw & R\=3, zB lonsists of a polynomials, U ¥ “ Brrreai by independent Yaw 2 ww 4 - 3\ => Pes \nas 2 pivet tolamr yi oO O-n 2 i fete, ve Le ebb § act Cinee. fy i in dagger da. =) {Pr » Pe fe lo Drnarcly im depen dtu, 2. Find the 8-coordinate vector of the polynomial p(t) = 7 — 3¢ + 92?. ee teat ef ,i-t Vy ia rad ! 4 i ae | ae le Solver 00-228 o \ 2 rd 42 ° | 11 0 3 | 0 93 = ale & 2 Shas o105\|.)/0 105 = tele: |€\ ob Qo1- 00 [- \ -) ? < a a 3. Verify your result in Part 2 by showing that p(t) is a linear combination of the basis poly nomials with the appropriate coefficients. 1 SEA gEE = aCirated EC 24a) (1-t-t') = 2 Bee eet ies} EL S451) = -~at +44"