Use the Matrix Exponential to find the general solution of the system x' = A x + b, where A = [2

Name: Use the Matrix Exponential to find the general solution of the system x' = A x + b, where A = [2 -1; 3 -2] and b = [0; e^-4t] The matrix A has eigenvalues lambda1 = -1, lambda2 = 1 and eigenvectors v1 = [1; 3], v2 = [1; 1].
Uploaded: 2023-08-31T17:01:50-08:00
Duration: 3 min 11 s
Channel: Sri K
Description: Use the Matrix Exponential to find the general solution of the system x' = A x + b, where A = [2 -1; 3 -2] and b = [0; e^-4t] The matrix A has eigenvalues lambda1 = -1, lambda2 = 1 and eigenvectors v1 = [1; 3], v2 = [1; 1].

Question

Use the Matrix Exponential to find the general solution of the system x&#x27; = A x + b, where A = [2

Sri K · Accepted Answer

1. First, we need to find the matrix exponential of A, which is denoted as e^(At). Since A has e

Question

Use the Matrix Exponential to find the general solution of the system x' = A x + b, where A = [2 -1; 3 -2] and b = [0; e^{-4t}] The matrix A has eigenvalues lambda_1 = -1, lambda_2 = 1 and eigenvectors v_1 = [1; 3], v_2 = [1; 1].

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