Consider a small particle moving under gravity and an electromagnetic field. We use the RK4 integrator to solve the differential question of this motion. m is the particle's mass, q is the charge, g is the gravity field, E is the electric field, and B is the magnetic field. The position is denoted as x = (1, y, z]E R. For the elements of g, E, and B, use g = 92, 93, 92]", E = [E., E., E,]", and B = [B., By, B.)". Define X = [, , t]" as the state space. 1. The first step is to make the state space form. * = AX +U (1) where A E R' R, and U ER" is a constant vector. Consider that q = 1.0 x 10-8 C, and m = 1 x 10-6 kg. Find the (4:7,4 : 7) elements of A and the (4 : 7) elements of U when g = (-1.2 x 10-3, -9.2 x 10-2,-1.5]" m/sec?, E = (1.23, 2.96,35.1] V/m, and B = (42.31 x 10-6, 10.83 x 10-8,36.13 x 10-6] T. A(4:7,4: 7) = A x 10 E x 10-7 I x 10 M X 100 B x 10-7 F x 10 J x 10-7 N X 10 C x 10-9 G x 10-7 K x 10 0 x 100 D x 10 H x 100 L x 10 P x 10 -9 (2) U (4:7) = Q x 10-2 Rx 10-2 S x 10 T x 100 (3) Consider a small particle moving under gravity and an electromagnetic field. We use the RK4 integrator to solve the differential question of this motion. m is the particle's mass, q is the charge, g is the gravity field, E is the electric field, and B is the magnetic field. The position is denoted as x = (1, y, z]E R. For the elements of g, E, and B, use g = 92, 93, 92]", E = [E., E., E,]", and B = [B., By, B.)". Define X = [, , t]" as the state space. 1. The first step is to make the state space form. * = AX +U (1) where A E R' R, and U ER" is a constant vector. Consider that q = 1.0 x 10-8 C, and m = 1 x 10-6 kg. Find the (4:7,4 : 7) elements of A and the (4 : 7) elements of U when g = (-1.2 x 10-3, -9.2 x 10-2,-1.5]" m/sec?, E = (1.23, 2.96,35.1] V/m, and B = (42.31 x 10-6, 10.83 x 10-8,36.13 x 10-6] T. A(4:7,4: 7) = A x 10 E x 10-7 I x 10 M X 100 B x 10-7 F x 10 J x 10-7 N X 10 C x 10-9 G x 10-7 K x 10 0 x 100 D x 10 H x 100 L x 10 P x 10 -9 (2) U (4:7) = Q x 10-2 Rx 10-2 S x 10 T x 100 (3)