- #1

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## Homework Statement

a = [1 1;4 1]

## Homework Equations

R = M^-1 * a * M

X = M * e^(R*t) * M^-1 * x

M is matrix of eigenvectors.

## The Attempt at a Solution

lambda = 3, -1

initial conditions:

x = [1 1]' at t = .1

eigenvectors:

k1 = [1 2]'

k2 = [1 -2]'

M = [1 1;2 -2]

M^-1 = [.5 .25; .5 -.25]

R = [3 0; 0 -1]

Solution:

X = [1 1; 2 -2] * [e^(3t) 0; 0 e^-t] * [.5 .25; .5 -.25] * x

How do I account for the fact t = .1? I keep seeing examples where t = 0. When I follow those examples I keep getting the wrong solution.