# Linear Algebra

## Assignments

4 Jan (Due 7 Jan) Solutions or counterexamples to, and new conjectures and frustrations about the four problems handed out in class (also available below in various formats)
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6 Jan (Due 14 Jan) pp 12-15: 1, 21, 22
8 Jan (Due 14 Jan) pp 19-23: 1, 20, 23, 24
11 Jan (Due 14 Jan) pp 20: 8(a-d), 9
13 Jan (Due 21 Jan) pp 31-33: 1, 2(c,e), 3(a,c), 8, 9, 11
15 Jan (Due 21 Jan) pp 38-39: 1, 6, 14
pp 52-53: 12, 13
18 Jan (Due 21 Jan) No class (Martin Luther King day)
20 Jan (Due 28 Jan) pp 51-55: 1, 4, 5, 7, 14, 27, 28
21 Jan (Due 28 Jan) (nothing more)
22 Jan (Due 28 Jan) First Hour Exam:
In class portion: Thursday, 28 Jan (12 - 12:50pm)
Take home portion: Out Thursday, 28 Jan; In Monday, 1 Feb
25 Jan (Due 28 Jan) Nothing again?! What a soft touch....
27 Jan (Due 4 Feb) pp 69-73: 1, 2, 3, 13, 16, 20
29 Jan (Due 4 Feb) Work on Exam
1 Feb (Due 4 Feb) Time to catch up from exam fever
3 Feb (Due 11 Feb) pp 78 - 79: 5a,c 7, 10
5 Feb (Due 11 Feb) pp 90 - 92: 10, 11, 16*
For 16, also show that there is a basis B of V so that the matrix of T with respect to B is diagonal, having r ones (where r = rank(T)) and n-r zeroes (where n = dim(V)) on the diagonal
8 Feb (Due 11 Feb) pp 99-100: 1, 12
10 Feb (Due 18 Feb) pp 99-100: 13, 15
12 Feb (Due 18 Feb) The following two problems:
For a function f in C2(R) (a real valued function with two continuous derivatives) define D(f) = f '' + 4f. Show that
a) D: P2(R) --> P2(R) is an isomorphism, but
b) D: C2(R) --> C2(R) is not an isomorphism.
15 Feb (Due 18 Feb) p. 170: 7d (find the solutions), 8a
17 Feb (Due 25 Feb) p. 156: 6 e,f (also find rank, nullity, range and nullspace)
18 Feb (Due 22 Feb) Second hour exam; in class and takehome
19 Feb (Due 25 Feb) p 108: 3(a,b,c), 4, 5
22 Feb (Due 25 Feb) pp 209 - 210: 1, 11, 25
p 217: 11, 14
24 Feb (Due 5 Mar) pp 247-248: 1, 3(a,b)
26 Feb (Due 5 Mar) pp248-250: 8, 17(a-d), 20
1 Mar (Due 5 Mar) pp 268 - 270: 1(a-g), 2(f,g), 7(see Example 7)
3 Mar none
5 Mar none
8 Mar none