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Find a fundamental matrix of each of the systems in Problems 1 through 8, then apply Eq. (8) to find a solution satisfying the given initial conditions. -3 -2 х, 3 -[-] 5. х x(0)

Find a fundamental matrix of each of the systems in Problems 1 through 8, then apply Eq. (8) to find a solution satisfying the given initial conditions. -3 -2 х, 3 -[-] 5. х x(0)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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Find a fundamental matrix of each of the systems in Problems 1 through 8, then apply Eq. (8) to find a solution satisfying the given initial conditions. -3 -2 х, 3 | 5. x' x(0) = | 9. 3 2 8. x' = -5 -4 -2 X, x(0) 5 3 THEOREM 1 Fundamental Matrix Solutions Let (1) be a fundamental matrix for the homogeneous linear system x' = Ax. Then the [unique] solution of the initial value problem x' = Ax, x(0) = Xo (7) is given by x(1) = (1)(0)-Xo. (8) I found this answer in the book 2 cos 3t -2 sin 3t 5. $(t) = -3 cos 3t +3 sin 3t 3 cos 3t +3 sin 3t 3 cos 31 – sin 3t x(t) = %3D -3 cos 3t + 6 sin 3t [ e3 -e3 el 8. Ф(() e-21 -e x(t) -e' +e-2 %3D 2r e-2
Transcribed Image Text:Find a fundamental matrix of each of the systems in Problems 1 through 8, then apply Eq. (8) to find a solution satisfying the given initial conditions. -3 -2 х, 3 | 5. x' x(0) = | 9. 3 2 8. x' = -5 -4 -2 X, x(0) 5 3 THEOREM 1 Fundamental Matrix Solutions Let (1) be a fundamental matrix for the homogeneous linear system x' = Ax. Then the [unique] solution of the initial value problem x' = Ax, x(0) = Xo (7) is given by x(1) = (1)(0)-Xo. (8) I found this answer in the book 2 cos 3t -2 sin 3t 5. $(t) = -3 cos 3t +3 sin 3t 3 cos 3t +3 sin 3t 3 cos 31 – sin 3t x(t) = %3D -3 cos 3t + 6 sin 3t [ e3 -e3 el 8. Ф(() e-21 -e x(t) -e' +e-2 %3D 2r e-2
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