Find the characteristic polynomial and the eigenvalues of the matrix. [::] 9 4 4 9 The characteristic polynomial is (Type an expression using A 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.

Find the inverse of the matrix, if it exists. Use the algorithm for finding A A = 15 3 14 Set up the matrix [A I]. [A I] = (Type an integer or simplified fraction for each matrix element.) by row reducing [A I].

Find the characteristic polynomial and the eigenvalues of the matrix. 5 [14] 7 The characteristic polynomial is (Type an expression using as the variable. Type an exact answer, using radicals as needed.)

decide if the given statement is true or false,and give a brief justification for your answer. If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false. Q. If two matrices A and B have the same characteristic polynomial,then Aand B musthaveexactlythesame set of eigenvalues.