Use Ackermann's Formula to find the observer gain L so that the eigenvalues of A-LC are placed at -3 and -12. Enter your answer as the value of the row 2 column 1 entry of L. Your answer must be a decimal number. Do not enter fractions. 2 A 4= (-1¹3) 03 C = (10)

x1 = x2 – 4x + 4x3 %3D 4 x½ = -3x2 - V3x, + V3x1 +X3 x3 = 7x2 - 2x1 Find the eigenvalues and eigenvectors by using the above equations.

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]