MATH 308 E: Homework

Homework 8:Mar 9
§ 4.4:14, 21
§ 4.5:6, 10, 14, 18
§ 4.6:22, 24, 30, 36
§ 4.7:5, 7, 17, 25

Make sure to keep a copy of this HW since it may not be graded on time for the final exam.

Homework 7:Mar 2
§ 3.7:2a, 3, 4, 10, 14, 19c, 21, 22, 28, 30, 34, 36, 44
§ 4.1:2, 10, 14, 17
§ 4.2:12, 18, 24, 25, 28, 30
§ 4.3:4, 12

This HW looks long, but the problems of 3.7 should be short.

Homework 6:Feb 16
§ 3.4:1, 9c, 11, 24, 34, 37
§ 3.5:4, 6, 9, 18, 26, 32, 33, 34
§ 3.6:4, 6, 10


Homework 5:Feb 9
§ 3.3:19, 20, 25, 32, 43, 48, 51, 52

Homework 4:Feb 2
§ 3.1:13, 16, 21, 22, 25, 28
§ 3.2:6, 10, 11, 21, 28, 33

Show that the subset \(U_3 \subseteq \mathbb{M}(3 \times 3) \) consisting of upper triangular matrices, that is, matrices of the form $$\begin{bmatrix} a_{11} & a_{12} & a_{13}\\ 0 & a_{22} & a_{23}\\ 0 & 0 & a_{33} \end{bmatrix}$$ is a subspace of \(\mathbb{M}(3 \times 3)\).
Homework 3:Jan 26
§ 1.7:12, 14, 20, 23, 50, 55, 56
§ 1.9:4, 8, 10, 20, 38, 39, 55, 69 70, 76

Comment on HW 3: When you do the problems on section 1.7, DO NOT use that nonsingular = invertible yet, as we don't see that until section 1.9. For the problems on section 1.9 you CAN use any of the equivalent definitions for nonsingular/invertible, use the one that helps you the most to solve the problem.


Homework 2:Jan 19
§ 1.5:6, 8c, 10c, 12b, 20, 24, 30, 48, 58, 59
§ 1.6:3, 11, 26, 27, 40, 44,47


Homework 1:Jan 12
§ 1.1:17, 29, 32, 35
§ 1.2:10, 21, 31, 35, 39, 49, 51
§ 1.3:4, 12, 18, 23, 24

Hints for HW:

§ 1.2 #49: Recall that we can write any 3-digit number as the sum \(100*x+10*y+z\) where \(x,y\) and \(z\) are the digits. For example \(308\) can be written as \(100*3+10*0+8\) in this case \(x =3, y = 0\) and \(z = 8\).

§ 1.2 #51: Let \(x_1, x_2, x_3\) be the initial amount of money players one, two and three respectively had. Also assume that player one losses the first round, player two the second round and player three the last round. Then subtract or add the amount of money each player would have in terms of the unknowns in each step. In the last step the amount of money each of the have would equal \(24\). These relations yield a linear system.