Suppose that A is 2×2 matrix with eigenvectors V1=[?1?, 2], V2=[?0?, 1] which correspond to ?1=3, ?2=-1 respectively. Find the general solution to the system X' = AX. none y = c1e^(3t)[?1?, 2] + c2te^(-t)[?0?, 1] y = c1e^(3t)[?1?, 2] + c2e^(-t)[?0?, 1] y = c1e^(3t)[?1?, 2] + c2e^(-t){?0?, 1] + t[?1?, 2]} y = c1e^(-t)[?1?, 2] + c2e^(3t)[?0?, 1]

          Suppose that A is 2×2 matrix with eigenvectors V1=[?1?, 2], V2=[?0?, 1] which correspond to ?1=3, ?2=-1 respectively.

Find the general solution to the system X' = AX.

none
y = c1e^(3t)[?1?, 2] + c2te^(-t)[?0?, 1]
y = c1e^(3t)[?1?, 2] + c2e^(-t)[?0?, 1]
y = c1e^(3t)[?1?, 2] + c2e^(-t){?0?, 1] + t[?1?, 2]}
y = c1e^(-t)[?1?, 2] + c2e^(3t)[?0?, 1]

Suppose that A is 2×2 matrix with eigenvectors V1=[?1?, 2], V2=[?0?, 1] which correspond to ?1=3, ?2=-1 respectively.

Find the general solution to the system X' = AX.

none
y = c1e^(3t)[?1?, 2] + c2te^(-t)[?0?, 1]
y = c1e^(3t)[?1?, 2] + c2e^(-t)[?0?, 1]
y = c1e^(3t)[?1?, 2] + c2e^(-t)?0?, 1] + t[?1?, 2]
y = c1e^(-t)[?1?, 2] + c2e^(3t)[?0?, 1]

Added by Domingo Q.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/09/2023

Step 1

First, we know that the eigenvectors and eigenvalues are given by: v1 = [2], λ1 = 4 v2 = [8], λ2 = -1 The general solution to the system X' = AX can be written as a linear combination of the eigenvectors multiplied by their respective exponential functions: y(t) Show more…

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Suppose that A is a 2x2 matrix with eigenvectors v1 = [2] and v2 = [8], which correspond to eigenvalues λ1 = 4 and λ2 = -1 respectively. Find the general solution to the system X' = AX. None y = Ce^(3t)v1 + C2te^(-t)v2 y = Ce^(3t)[2] + e^(-t)[C] y = Ce^(3t)[2] + se^(8t)[2] y = Ce^(-t)[2] + C2e^(3t)[8]