



0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
Question 19 (1-1 Find the eigenvalues and corresponding eigenvectors for the matrix 0 6 2 0-19 Selected Answer 21 = 8, x= (0,1,1) 12 = 7, x2 =(-1, 12,-6) d. hg = 1, 13 = (1,0,0)
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
1 -1 1 Find the eigenvalues and corresponding eigenvectors for the matrix 0 6 2 0-19 Selected Answer: 21 = 8, x1 = (0,1,1) 12 = 7, 12 =(-1, 12, -6) d. 13 = 1, 13 = (1,0,0)
.3 Suppose the eigenvalues of a 3x3 matrix A are A, 4, , and A 6' %3D with corresponding eigenvectors v,= V2= and v Let -2 -5 6. 11 Find the solution of the equation x Ax, for the specified x, and describe what happens ask-o. 13 Find the solution of the equation X1AX Choose the correct answer below. 4. 1. O A. X=2.(4)* +3. -4 1. 6. -5 -2 -3 O B. X=2.(4)* 0 +3. 1. -5 6. 11...
(23). (15 Marks). Suppose A has eigenvalues 11 = 3, 12 = 1, 13 = 0) with corresponding eigenvectors 0 0 2 = [1] 12 8) 23 = (a) (5 points). How do you know that the third column of A contains all zeros? (b) (10 points). Find the matrix A.
Solving 1. Let -Ar, A constant, with real and distinct eigenvalues 3-1 0 2-2 3 A 2 0 0 (a) Find the eigenvalues and the corresponding eigenvectors for the matrix A. (b) Use (a) to write down a fundamental matrix Φ(t) for the system z' = Az, and use Φ(t) to calculate the solution of this system that satisfies the initial condition (0)0
2d
and 4b
[2 リ 5 0 -6 200 x(0)=10 x' e2 0 0 |-6-1 3 0 42 0-1-2 x, 43,1 0 0 (d) x' = ' x' (c) x'=12-1-2|x; 2. The matrices in the following systems have complex eigenvalues; use Theorem 2 to find the general (real-valued) solution; if initial conditions are given, find the particular solution satisfying them. 1-x, x(0)-1 (b) x, = (a) x' = X; 0 20 x(0)-|2 이 x, (d) x'=1-20 (c) x' =10-1-6|x; L0...
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 2 -2 7 0 3 -2 0 -1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (91, 12, 13) = 1, 2, 4 the corresponding eigenvectors X1 = x X2 = X3 =
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0-1 0-1 0 -107 Find the characteristic polynomial of A. far - 41 - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12, 13) = Find the general form for every eigenvector corresponding to 11. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x2 = (0.t,0)...