Find the eigenvalues and eigenvectors of the matrix A - = -3 10 2 —4
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
Find the eigenvalues and associated eigenvectors of the matrix Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A= Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A = b) Find the projection of the vector 7 = (1, 3, 5) on the vector i = (2,0,1). c) Determine whether the given set of vectors are linearly independent or linearly dependent in R" i) {(2,-1,5), (1,3,-4), (-3,-9,12) } ii) {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) }
$$ \text { For the matrix } A=\left[\begin{array}{ccc} 6 & 9 & -10 \\ 6 & 3 & -4 \\ 7 & 7 & -0 \end{array}\right] \text {, find eigenvalues and eigenvectors. } $$
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. -4 4-6 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) A1, ?2, ?3) the corresponding eigenvectors X1 =
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b) Solve the initial value problem: dx/dt = 4x + 2y dy/dt = 3x - y with x(0) = 0, y(0) = 7
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3 Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it is possible to diagonalized, then diagonalize the matrix. If it is not possible to diagonalize, then explain why? Show all the work. (20 points) 54 -5 A = 1 0 LO 1 1 - 1 -1