a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3 - i A1 = , V1 = 5 -3 + i A2 = -i , V2 = b. Find the real-valued solution to the initial value problem x = 3x1 + 2x2, х, — —521 — З22, x1(0) = 1, x2(0) = -5. Use t as the independent variable in your answers. r1(t) = -3 cos(1) + sin(t) Фо(t)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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a. Find the eigenvalues and eigenvectors for the coefficient matrix.
-3 - i
A1 =
, V1 =
5
-3 + i
A2 =
-i
, V2 =
b. Find the real-valued solution to the initial value problem
x = 3x1 + 2x2,
х, — —521 — З22,
x1(0) = 1,
x2(0) = -5.
Use t as the independent variable in your answers.
r1(t) = -3 cos(1) + sin(t)
Фо(t)
Transcribed Image Text:a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3 - i A1 = , V1 = 5 -3 + i A2 = -i , V2 = b. Find the real-valued solution to the initial value problem x = 3x1 + 2x2, х, — —521 — З22, x1(0) = 1, x2(0) = -5. Use t as the independent variable in your answers. r1(t) = -3 cos(1) + sin(t) Фо(t)
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