Solve the system
 x 0 
 01
 x 2 =
 x 03
 6 3 6   x 

  1
 1 4 2   x 2
−2 −2 −1  x 3
 x (0)  −5
 1   
 x 2 (0)  =  2 
 x 3 (0)   1 
The matrix has eigenvalue 3 of multiplicity 3, with two independent
−2
−1
 
 
eigenvectors  1  and  0  .
 
 
0
1
 
Which of the following techniques do you feel you most need to review?
A
Finding eigenvalues/eigenvectors
B
Row reduction
C
Computing matrix inverse (2 × 2 and 3 × 3)
D
Partial fractions
E
Integration by parts
Solve the system
" 0# "
# " # " 3t #
1 2 x1
x1
12e
=
+
x 02
4 3 x2
18e2t
Solve the system
" 0# "
# " # " −t #
x1
−2 1 x 1
2e
=
+
x 02
1 −2 x 2
t