Q1:

Find the characteristic polynomial of the matn'x, using either a cofactor expansion or the special formula for 3x3 determinants. involved] 40 0 92? 40 3 The characteristic polynomial is :|. (Type an expression using 1 as the variable.) For the matrix, list the real eigenvalues, repeated according to their multiplicities. Co w NNO ooo O 8 0 0 CO The real eigenvalues are. (Use a comma to separate answers as needed.)For the matrix. list the eigenvalues, repeated according to their multiplicities. 3 0 0 0 9 9 0 0 0 2 3 0 6 8 '." 8 The eigenvalues are D (Use a comma to separate answers as needed} 5 -4 8 It can be shown that the algebraic multiplicity of an eigenvalue ^ is always greater than or equal to the dimension of the eigenspace corresponding to A. Find h in the matrix A below such that the eigenspace for 2 = 5 is two-dimensional. 0 1h A= O 0 5 2 0 0 The value of h for which the eigenspace for ^ = 5 is two-dimensional is h =