questions below:

Find the characteristic polynomial and the eigenvalues of the matrix. - 2 - 3 5 -5 . . . The characteristic polynomial is. (Type an expression using ) as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) O B. The matrix has no real eigenvalues.A particle moving in a planar force field has a position vector x that satisfies x' = Ax. The 2 x 2 matrix A has eigenvalues 4 and 3, with corresponding eigenvectors v1 andve = 7 .Find 23 the position of the particle at time t assuming that x(0) = Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or simplified fractions.) O A. X(1) = O B. X(1) =3 1 Let the matrix - 2 5 act on C2. Find the eigenvalues and a basis for each eigenspace in C2. . . . Select all that apply. 1 - i A. 2=1-41; v= 1 - 2 B. 2=4 - i; v= 1+ i O c. 2=4- i; v= 2 D. 2= -4+ i; v= 1+ i DE. 2=4+ i; v= 4 OF. 2=1+4i; v= i 2 1 - i G. 1=4+ i; v= 2 1+ i OH. 2= -4- i; v= 4