# Homework

Written homework should be turned in to the homework boxes outside of Kemeny 108 by 3:30pm each Wednesday (unless otherwise stated).

No late homework will be accepted. However, your lowest homework score will be dropped.

Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, you must write the solution up on your own. Please acknowledge any cooperative work at the end of each assignment.

Assignment Due Date Problems
HW 1 Wed, April 04 §1.1: #7, 9, 12, 24
§1.2: #5, 12 (Hint: do (b) first), 13
§1.3: #8, 14
§2.1: #15, 17, 30, 33
§2.2: #8, 18, 25
HW 2 Wed, April 11 §2.3: #2, 4, 8 (Hint: Solve 8 (c) numerically.)
§2.4: #11, 14, 22, 25, 28, 33
§2.5: #4, 12, 15
§2.6: #2, 14, 16, 24, 27

HW 3 Wed, April 18 §3.1: # 11, 22, 23, 27
§3.2: # 10, 12, 19, 22, 24, 39
§3.3: # 1, 5, 11, 20, 26, 28
§3.4: # 6, 13, 21, 28, 37
HW 4 Wed, April 25 §3.5: # 9, 14, 16, 18, 29, 35
§3.6: # 4, 10, 15, 21, 22, 23
§6.1 # 5, 14, 16, 24
§6.2 # 6, 16, 26, 29, 32
HW 5 Fri, May 04
3:30 pm
§6.3 # 18, 21, 25
§6.5 # 8, 14, 25
§6.6 # 1, 2,  5, 10, 16

HW 6 Wed, May 9
§7.1 # 3, 5, 7,
§7.1 # 15, 16  ( In these two questions first rewrite the system in the
matrix form, then restate the question in this form and
§7.3: # 11, 25, 29, 31, 34

HW 7
Wed, May 16
§7.4: # 2 (only a, b, c.  See hint below),  5, 6 (see note-1 below)
§7.5: #  12, 18, 25  (see note-2 below)
§7.6: # 11(a, b, c),  14
§7.8: # 10, 15, 18 (only a, b, c, d)

Hint: For simplifications you can use the fact that elementary row addition operations (adding a multiple of a row to another) don't change the determinant.
Note-1: In 7.4 #6 part (b)  is about linear independence of vectors (not functions).
Note-2: For 3x3 matrices you can use computer to calculate eigenvalues and eigenvectors
HW 8 Wed, May 23
§7.8: # 10, 21 (only a,b,c),
§7.8: Solve the Question below
§10.1: # 4, 8, 15, 18
§10.2: # 8, 19 (a, b),  21 (a, b)

Question
(a) Solve §7.8  #22 part (a)
(b) Solve §7.8  #22 part (b)
(c) Solve §7.8  #22 part (c)
(d) Using previous parts  to calculate the general solution of $x'=A x$ where  $A=T J T^{-1}$ and  $$T=\begin{pmatrix}a & b & 0\\\ 0 & c & d\\\ 0 & 0 & f\end{pmatrix} \qquad J=\begin{pmatrix}\lambda & 1 & 0 \\\ 0 & \lambda & 1\\\ 0 & 0 & \lambda\end{pmatrix}$$
HW 9
Don't
return

§10.2: # 28
§10.3: # 2, 13, 15, 17
§10.4: # 9, 13, 14
§10.5: # 2, 8, 9, 13
§10.7: # 12, 13, 14