Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. A = 322 1 2 1 = 112 2 1 1 1 1 0 - 1 0 - 1 500 0 1 0 001 1 4 1 4 1 4 1 4 1 4 3 1 4 3 4 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use comma to separate vectors as needed.) O A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is OB. In ascending order, the two distinct eigenvalues are >₁= and λ = OC. In ascending order, the three distinct eigenvalues are ₁ -C Bases for the corresponding eigenspaces are and { }, respectively. ^₂=₁ and 23 =Bases for the corresponding eigenspaces are 1 and , respectively.

Find a basis for the eigenspace corresponding to the eigenvalue. 4 - 3 3 A = 6 , 1 = 3 - 2 -6 -3 A basis for the eigenspace corresponding to 1 = 3 is { }. (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Use a comma to separate answers as needed.)

Matrix A is factored in the form PDP¯1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 20 - 16 – 40 - 1 6 0 0 0 0 1 A= 8 6 32 1 060 2 1 8 0 0 6 1 0 0 0 0 2 -10 - 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, À = A basis for the corresponding eigenspace is { }. O B. In ascending order, the two distinct eigenvalues are = and 2 = Bases for the corresponding eigenspaces are { } and {}, respectively. O C. In ascending order, the three distinct eigenvalues are , = 12 = Bases for the corresponding eigenspaces are {}. { }, and {}, respectively. and A3 = Click to select and enter your answer(s). DELL

Find the matrix A of the quadratic form associated with the equation. 4x² - 6xy - 4y² + 6 = 0 A = 4 -3 P = -3 -4 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) λ = 5, -5 Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) [1,0], [0,1]

For the matrix, list the real eigenvalues, repeated according to their multiplicities. The real eigenvalues are (Use a comma to separate answers as needed.) 8-40 8 6 5 -5 03 8 00 8 0 0 0

Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 033 0 3 3 3 3 λ; = For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x;) =