Need help 1-6

For problems 1-8. we will use The matrices C = 13 2 0 1 0 -2 Recall from Thursday's class that if i is on eigenvector of a matrix M, with eigenvalue 1, then * ( ) = velt solves * (7 )= Mx ( ). If M has real entries and I is no toal reale eigenvalue, so IEatbi and bto then we can use Relight) and I'm(velt) to build two finearly independent solutions to x' (t ) = MY ( ): Ya(t ) = eat ( Re() cos(bt) - I'm (v ) sin (bt)) and yact ) = eat ( Im (v ) cos (bt ) + Relv ) sin (bt). ( using 1 = atbi ) 1. Find a basis for the set of solutions to x'l) = Ax(). 2. Find a basis for the set of real-volved solutions to x'(t)= Box (+). 3. Find a basis for the set of real-volved solutions to x'lf) = (xCD. 4 . Find the unique solution to * ' ()= AF ( ) satisfying $ 10)-13] 5. Find the unique solution to *'()= AX( ) satisfying $(0)= (4] 6. Draw the graph of the parametric function ( * (+) ( * 2 (t ) in R , where (x , ( + ) ) x 2 ( + ) was your solution to problem 4. ( Note: you do not need to