Find the matrix A of the quadratic form associated with the equation. 3x²8xy - 3y² + 12 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) λ = 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.) P

For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) -1 0 0 2 15 501 P = A = ↓↑ Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

Diagonlize the matrix if possible. the eigenvalues are as follows λ=3,1 7 4 16 2 5 8 -2 -2 -5

Please help, in order to review for a test:

3. Find the Eigen value of the following matrix: (3 1 1) B = (2 4 2 \1 1 3/

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 A, find (if possible) a nonsingular matrix P such that P1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 100 15-1 L-30 5. A= 41 p-¹AP = Verify that PAP is a diagonal matrix with the eigenvalues on the main diagonal. 2 000 000 11

Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated list.) 50 1 0 1 2 0 0 2