In Problems 1-6 write the linear system in matrix form. 6. dx - 3x + 4y + etsin 21 dt dy 5x + 4z + 4ecos 2t dt dz = y + 6z - et dt = In Problems 7-10 write the given system without the use of matrices (2 10. * (T) = (? -7)(3) + (*)sine + (2,71)" + In Problems 11-16 verify that the vector X is a solution of the given system 10 16. X' = 11 -20 sint sin : - cos -sint + cost 3 0 X X -1 26. Prove that the general solution of x = (-} -)x +(+)2 + (-4)=+(-3) on the interval (-) is 4 다 x = c(-1 - vz)eve + c(-1 + vale-v> cil- vs +()*+(-) + () + In Problems 1-12 find the general solution of the given system. 7. B 山山山山山 dx = x + y - 2 dt dy dt dz = y z dt 11 2y In Problems 13 and 14 solve the given initial-value problem. ( 11 4 14. X' = 0 2 0 X, X(0) = 3 1 1 1 6 31. Show that the 5 x 5 matrix 12 1 0 0 0 0 2 0 0 0 A = 0 0 2 0 0 0 0 0 2 1 0 0 0 0 2 N 7 has an eigenvalue 1 of multiplicity 5. Show that three linearly independent eigenvectors corresponding to 11 can be found. In Problems 5-8 use (1) to find the general solution of the given system. 5. X' = (2) X ४ In Problems 9-12 use (5) to find the general solution of the given system. 10. X' = = (; 2)x + () : X + q 0 4