I need solve this assignment

Work Problem 1 (20 points): a) Given the vectors in R3 v1=(11 3),v2=(131).v3=(-31 1) Using the system of linear equations determine whether the given vectors are linearly independent. b) Determine whether given vectors p1 (t) = 21'2 t, p20) = t2 3, p3(t) = tin P2 are linearly independent. Work Problem 2 (20 points): Given the set of the vectors in M22 s=[(;:).(;:).(22}[::)l a) Create the system you need to solve to determine whether S is linearly dependent in M22. b) Determine whether Sis linearly dependent. Work Problem 3 (20 points): a) Consider the set S={t2+1, t2+t, t+1}. Detrmine whether p(t) = 3t2 - SH 3 belongs to span 8. b) Determine whether {t2 + 1, 22 - t, H 1} is a spanning set