For the system X' = AX, if the eigenvector associated with the eigenvalue (-2 + i) is L. Then, which of the following is considered as a fundamental matrix for 1+il that system? 2e-2t cost a) 2e-2t sint -e-2t sint)] -2t cost et cost b) Fetcost -e'sint! etsint -2t cost e-2t sint -2t (cost – sint). e (cost + sint) e 2e-2t sint d) -e-2t(cost + sint) e-2t(cost – sint). 2e-2t cost

Q2) for the following Matrix ‘A°, Please determine the following: a. Eigenvalue of A b. Eigenvector of A, make your answer for a. and b, in the unit vector form.

Good evening, I found the Eigenvalues to be Lamda = 0, 2, -4. I really only need help with the Eigenvector for Lamda=2. Are there two free variables? I don't know how to intrepret the system. Thanks!

Compute the matrix exponential eat for the system x' = Ax given below. x₁ = 41x₁40x2, x 2 = 38x₁ - 37x2 1 eAt (Use integers or fractions for any numbers in the expression.)

Please help me solve this. I got to all three eigens are equal to zero by doing subtraction of 5(first equation)-(third equation) and 3(first equation)-(second equation) and then solced out for my "a" "b" and "c" values. where did I go wrong here?? only HANDWRITTEN answer needed ( NOT TYPED)

For the matrix A , there is an invertible matrix P such that P^(−1)*AP = D, where D is a diagonal matrix with the eigenvalues of A on the diagonal.  Calculate the matrix product P^(-1)*AP

- (1-3). Determine the eigenvalue and corres- 3. a) Given the matrix A = ponding eigenvector and generalized eigenvector of A. b) Determine the general solution of the system of linear differential equations: x₁ = I₁=I₂ x₂ = x1₁+3x₂

(a) Determine the characteristic equation and eigenvalues A in the system (³) () - ^ (). = A (b) Show that the vectors a = 7+37+5k, 6=-27+47-6k and = -37+7-11k are coplanar.

A 2x2 matrix has trace -13. One of its eigenvalues is -9. What is the other eigenvalue?

The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 8x₁ + 3x₂ + 8x3, x'₂ = 3x₁ + 13x₂ + 3x3, x'3 = 8x₁ + 3x₂ + 8x3 What is the general solution in matrix form? x(t)