Question 1 1 pts Let V be the set of solutions to y" - y = 0. Is V a vector space? O no (V is not closed under linear combinations) Yes Question 2 1 pts Let V be the set of solutions to y" + 4y = 0. Is V a vector space? O Yes O no (V is not closed under linear combinations) Question 3 1 pts 1 Let V be the set of vectors in R such that X3 1 + x2 +23 = 0. Is V a vector space? O yes O no (V is not closed under linear combinations) Question 4 1 pts 1 Let V be the set of vectors 2 in R such that x] + 2 + 3 = 1. Is V a vector space? yes O no (V is not closed under linear combinations)Question 5 1 pts Let V be the set of vectors of the form a where a. and b are b real numbers. Is V a vector space? 0 no (V is not closed under linear combinations) 0 yes Question 6 1 pts Let V be the set of all differentiable functions (meaning functions that are differentiable everywhere in R). ls V a vector space? 0 no (V is not closed under linear combinations) 0 YES Question 7 1 pts Let V be the set of all solutions to the differential equation 34" + y = cos(t). IsV a vector space? If not, which conditions fail? (You must choose all conditions that fail in order to receive full credit.) 0 no (V is not closed under linear combinations) 0 Yes Question 8 1 pts Determine whether the system has one solution, infinitely many solutions, or no solutions. In the first two cases, find the solution(s) as well. (This is from last week, so it's essentially free points.) 5x + (1 - 32)y = 0 (-1 -32)x - 2y = 0 O The solution is c=-1+ 32 y = 5 O No answer text provided. There is no solution. O There are infinitely many solutions, given by x = -(1 - 32)y/5 y = y Question 9 1 pts Are the following vectors linearly independent, and if not, what coefficients c1, C2, C3 give the non-trivial linear combination O yes (c1 = C2 = C3 = 0 is the only solution) O no (c1 = 1, C2 = 1, C3 = 1) O no (c1 = -1, C2 = 2, C3 = 0) O no (c1 = -1, C2 = 0, C3 = 1) Question 10 1 pts Are the following vectors linearly independent, and if not, what coefficients c1, C2, C3 give the non-trivial linear combination? O no (c1 = 1, C2 = 1, C3 = 1) O no (c1 = -4, C2 = -4, C3 = -2) O no (c1 = 0, C2 = 1, C3 = -1) O yes