# Bonus Homework 
> 
#  Name:
# 
# Note:
# This bonus homework counts as three quarters of a homework.  It is
# designed to help raise the grades of people who did not do well on one
# of the other homework assignments.  How it works:  your lowest
# homework grade will be replaced by:   (1/4 * old_grade) +
# grade_on_bonus(out of 6).   Where each old homework is scaled to be
# out of 8 points.
# 
#  Instructions:
# -All work must be done independantly -- you may not work in groups on
# this one.
# -Show all your relavent work and/or Maple commands. No work => Few
# points.
# 
# Due:  Thursday May 10th, 13:00. Submit via sumit.ncsu.edu.
> with(linalg):
# 1. For the following, determine if the given function T is a linear
# transformation; if it is linear, find the matrix A such that T = fA.
> 
#  a) T(x,y,z) = (z-2 y ,x-y)
> 
> 
# b) T(x,y,z) = x + y + z 
> 
> 
#  2. For the matrix
>  A := matrix([[1, 7, 33, -28], [1, 0, -10, 16], [0, 1, 6, -6], [0, 0,
> 1, -2]]);

                          [1    7     33    -28]
                          [                    ]
                          [1    0    -10     16]
                     A := [                    ]
                          [0    1      6     -6]
                          [                    ]
                          [0    0      1     -2]

# a.  Find the characteristic polynomial of A in factored form, without
# using the charpoly command. 
#      Hint:  You can use the factor() command to find its factors.
> 
> 
> 
# b. Find the eigenvalues of A by finding the roots of the
# charactaristic polynomial in (a).
> 
> 
> 
> 
#  3.  For the system of differential equations:
#             du/dt = 2w - u
#             dv/dt = 2v - w
#             dw/dt = -6 w + v 
#       do the following: 
> 
# a.Use the method from class to find the general solution to the system
# of differential equations. 
> 
> 
> 
> 
#  b. Find the particular solution that satisfies the initial conditions
# u=1, v=2, and w=1 when t=0.
> 
> 
> 
>