Math 115A
Homework 1 Comments
I graded 10 of the problems:
Section 1.2: 9, 11, 13, 14, 17
Section 1.3: 2, 10, 18, 19, 22.
Each problem is worth 2 points. A grade of 0 indicates no solution or a substantially wrong solution. A
grade of 2 indicates a correct or nearly correct solution. Otherwise the grade given is 1.
If you believe a problem was misgraded, or I made some addition or other error, please write a short note
explaining the situation, attach it to your homework, and return it to me (either in person, in my mailbox,
or under my office door). I’ll take a look and afterwards leave your homework in a box outside my office.
The following are comments and occasionally solutions for the graded problems.
1.2
9. For the corollaries, you assume there two of the item in question and show that they are in fact equal.
For example assume there are two additive identitities 0 and 0 ; from VS3 we then have 0 + 0 = 0
and 0 + 0 = 0 . By VS1 0 + 0 = 0 + 0 and so it follows 0 = 0 .
For corollary 2, some people used the notation

x
for the additive inverse, even though it is really
not defined until we’ve used corollary 2 to show that the inverse is unique. However I accepted it as
just a notation for “one of” the additive inverses.
For 1.2c, most people used the trick that
a
0 =
a
(0 + 0) =
a
0 +
a
0 and cancelling by 1.1 we get
a
0 = 0.
11. This was a giveaway. As long as you looked like you went through the axioms and made a reasonable
effort I gave full points.
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 Spring '09
 Liu
 Math, Linear Algebra, Algebra, Vector Space, additive inverse, VS5, W1 ∪ W2

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