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| + | I have a question on the last 2 homework problems in section 7.4 #32, 34. How exactly do we determine if something is a vector space? Do all vectors have to be linearly independent? I know in class we went over a couple of test to determine if vectors are a subspace. Does that come into play? Thank you. | ||
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[[2013_Fall_MA_527_Bell|Back to MA527, Fall 2013]] | [[2013_Fall_MA_527_Bell|Back to MA527, Fall 2013]] | ||
Revision as of 11:08, 27 August 2013
Homework 1 collaboration area
Feel free to toss around ideas here. Feel free to form teams to toss around ideas. Feel free to create your own workspace for your own team. --Steve Bell
By the way, I sign my name at the end of a post by typing three tildes in a row, and the Rhea puts my name in for me. - Steve Bell
Here is my favorite formula:
$ f(a)=\frac{1}{2\pi i}\int_\gamma \frac{f(z)}{z-a}\ dz. $
This is a test formula:
$ A \vec x= \vec b $ - Eun Young
People have noted an error in the solutions in the back of the book. This from Jeff R.:
For Section 7.2 problem 29, they have the profit vector as
[85, 62, 30]
but the problem defines it as
[35, 62, 30]
which obviously gives a different answer. Just wanted to make you aware of the mistake. (Thanks, Jeff. Steve Bell )
Question from a student :
I have a question on the Kirchoff law problem, section 7.3 problem 18. On the loop portion of the defining equations, relative to a clockwise direction, I find the equation of the right loop to be -12 I2 + 8 I3 = -24. Is this correct to assume the I2 term is negative due to the counterclockwise flow of I2, as with the voltage term?
Answer from Eun Young :
Yes, it's correct and it's same as $ 12 I_2 -8 I_3 = 24. $
Remark from Steve Bell :
I remember from my engineering days that engineers make one convention about the sign of the increase in voltage around a loop in Kirchoff's Laws and physicists make the opposite convention, so this might be a cultural thing. The important thing to understand here is the math.
Question from a student :
That equation is the same thing I got, I just took a different direction for my KVL around the loop (e.g. $ 12 I_2 - 8 I_3 = 24 $). However, I don't fully understand what your question is. I do however have a question on p. 287 #12, 14, and 15. Is the book looking for a rigorous proof or just an example of this property? --Ryan Russon 18:48, 25 August 2013 (UTC)
Answer from Eun Young :
When a problem asks you to show or prove something, you need to provide proof. When a problem asks you to disprove something, you need to give an example. Hence, you need to prove #12, 14, and 15. There is a theorem about rank in sec 7.4. With this theorem, you can show the properties in #12, 14, and 15 easily.
Remark from Steve Bell :
Perhaps the word "proof" is overkill here. I would like you to be able to explain in words why something is a general fact, much like I do in class. It doesn't need to feel like a mathematical proof, but it does need to be convincing.
From --Ryan Russon
Thanks for the clarification. I was on my way to working on a very rigorous proof and then wondered if all the work was necessary.
Question from a student :
I have a question on the last 2 homework problems in section 7.4 #32, 34. How exactly do we determine if something is a vector space? Do all vectors have to be linearly independent? I know in class we went over a couple of test to determine if vectors are a subspace. Does that come into play? Thank you.
