Exam 2 with Solution Key - Linear Algebra | MATH 201, Exams of Linear Algebra

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1. Recall that P3 stands for the vector space of polynomials of at most second degree Py = (p(x) =a) +agr+aga*: a, € R, i= 1,2,3}. Let 3 paz) =x" —-1 Pilz) =1—2, and denote S = Span{pj, pa, ps}. (a) Are py,y2, and ps linearly independent as elements of Ps? (b) Find the basis of 9 as a subspace of Py. (c) State the dimension of S. BG> C,-0yT © rae Hee gelycemiols a5 clamn wee . BRO® => (2, 1-1)" (B) Giron a mek rix ond reducer to REF, Ps) 2 C-i, 0,17 \ Oo -] j; o -\ ' o -\ -“( [I oO Rr @, 22, oO | -| oO V. =| o-| I o-l 1 / Ri xk2ks | o O e @) Nay since Here 18 A row of Berets in REP, +e vector S are Vieear hey deeerdee ) Since the Ges) ad second o (uamnrs cantar , leading dee t tle basis consists af the firgsh and second arigine{ column veclucs 7 ,-1,0)7, (o,) “1y7 a) Stace the basis Contacas tws vecterS, dim S22.