 
Summary: Mathematics 3C, Fall 2011
Worksheet 1, TA Grace Kennedy
NAME:
MY WEBSITE: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Write clearly and justify every step as if this were an exam.
Consider the following system of two differential equations:
x (t) = x(t)  2y(t)
y (t) = 2x(t) + 4y(t)
Let ^v (t) =
x (t)
y (t)
and ^v(t) =
x(t)
y(t)
.
1. The coefficient matrix is the matrix A so that ^v (t) = A^v(t). Write the
coefficient matrix for this system. (You find this in exactly the same way
as you would for a system of linear equations.)
2. Just like in calculus, there is no change when the derivative is zero! Use
Gaussian elimination to solve A^v(t) =
