Question 1 1 pts What is the system of ODEs a; = 3x1 - x2 + cos(t), a2 = 21 + 4x2 + t - e t in matrix form X' = AX + G? ox - (2 7 ) x + (cos( ) Ox' = (3 1 x + 05 () " = (1 37) x + ((0(2. ) O X' cos ( t ) it - et 1 ) x + ( 2 ) Question 2 1 pts Suppose that X1, X2, and X3 solve the IVP's X' = AX1 , X1(to) = U1 X'2 = AX2, X2(to) = U2 X? = AX3 , X3(to) = U3 . Find a solution to the IVP X' = AX, X(to) = c1 U1 + c2 U2 + c3 U3 . O X = c1X1 + c2X2 + C3X3 O X = qj U 1 + c2 U2 + (3 UsQuestion 3 1 pts Consider the system X' = AX, where A is a n x n matrix with constant entries. If I give you n + 1 solutions to the system - say X1, X2, - - - 5Xn+1 - can the X,- be linearly independent? Answer true if they can be linearly independent. False otherwise. True Q False Question 4 1 pts Consider the system X' = AX, where A is a n x n matrix with constant entries. If I give you 71. solutions to the system - say X1, X2, ~ - - , X\" - and | tell you that these X,- span all solutions to the system. Are they linearly independent? Answer true if they are. False otherwise. 0 True False Question 5 1 pts Consider the system X' = AX, where A is a n x n matrix with constant entries. If I give you n i 1 solutions to the system - say X1, X2, - - - 5Xn+1 - and | tell you that these X,- are linearly independent, can these X,- form a basis of all solutions to the system? Answer true if they can, false otherwise. 0 True False