Finding the fundamental matrix where psi(0) = the identity matrix

capertiller

1. The problem statement, all variables and given/known data

If I have a solution to a system of first order linear equations: $<x,y> = c_1 e^{-3t} <1,-1> + c_2 e^{-t} <1,1>$ , how do I find the fundamental matrix psi(t) so that psi(0) = I ?

2. Relevant equations

3. The attempt at a solution

$psi(t) = <<e^{3t}, e^{-t}>, <-e^{-3t}, e^{-t}>>$
$psi(0) = <<1, 1>, <-1, 1>>$

This is clearly not the identity matrix.
Now what?

Related Calculus and Beyond Homework News on Phys.org

lanedance

Homework Helper
just an idea but you have two linearly independent basis vectors call them u1, u2

could you take a linear comibination of your vectors such that
v1=au1+bu2 gives v1(0) = <1,0>
and
v2=cu1+du2 gives v2(0) = <0,1>?

then could you use those basis vectors to write the reuired fundamental matrix?

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving