Consider the matrix A. 400 A: 130 231 Find the characteristic polynomial for the matrix A. (Write your answer in terms of A.) Find the real eigenvalues for the matrix A. (Enter your answers as a comma-separated list.) A, = E Find a basis for each eigenspace for the matrix A. :" (smallest eigenvalue) ii if 4 ii if 4 (largest eigenvalue) Jill Consider the matrix A. 40 0 A: 13 0 231 Find the characteristic polynomial for the matrix A. (Write your answer in terms of .1.) 43 + 6x2 51 12 Find the real eigenvalues for the matrix A. (Enter your answers as a comma-separated list.) .1 = 1,3,4 J Find a basis for each eigenspace for the matrix A. E (smallest eigenvalue) D (largest eigenvalue) D Now, Basis of eigenspace for 1= 4 for this , AX = 1 x X = NLES =) Ax = 4X - ) 1400 1 30 - 23-1 42 = ) 401 = 471 21 = 4 =) 21 + 3 4 = 4y - 2 n t 3 n - 2 = 42 - 2x1-+ 34 -Z = 42 " .. X = y = 52 52 5 5z 5 .: Basis is Leg Here, Basis of eigenspace for 1=y isf for largest eigenvalue