Find the eigenvalues À, and , and corresponding vectors v, and v, for each matrix A. Determine the equations of the lines through the origin in the direction of the eigenvectors v, and v2, and graph the lines together v eigenvectors v, and v, and the vectors Av, and Av,. A = The greater eigenvalue , is and the corresponding eigenvector is v, = The lesser eigenvalue i, isand the corresponding eigenvector is v, = Determine the equation of the line through the origin in the direction of the eigenvectors v,. (Type an equation in terms of x, and x,.) Determine the equation of the line through the origin in the direction of the eigenvectors v2. (Type an equation in terms of x, and x2.) Graph the lines together with the eigenvectors v, and v, and the vectors Av, and Av,. Choose the correct answer below. O A. OB. Oc. OD. ド2 4- 2 イー

Let A be a 3x3 symmetric matrix. Assume that A has two eigenvalues: A₁ = 0, and X₂ X2 independent eigenvectors of A corresponding to X₁: 1 H 1 1 Find a non-zero vector V3 which is an eigenvector of A corresponding to A₂. Enter the vector V3 in the form [C₁, C₂, C3]: V₁ = 9 V₂ = 2 2 0 2. The vectors V₁ and V₂ given below are linearly

Find the matrix A of the quadratic form associated with the equation. 2x² 3xy - 2y² + 10 = 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 matrix C, find the associated eigenvalues. c=15₁ 31 C -1 01 and 5 O4 and 3 O-5 and 2 O4 and 6