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My math homework... - love like me ・ 日記
non solum memento mori, memento vivere sed etiam
My math homework...
気持: *facepalm*
I am stupid. At least when it comes to math. Granted, it's not as if I have some sort of learning disability or anything. I'm better at math than most people, but I still feel stupid, because among my circle of friends, I'm the one who is the least good at math. This is what happens when your friends are all compsci geeks.

So, in a plea for help to those of you who can help, and in a plea for pity, commisseration, or even awe from those who won't have the faintest idea what is going on here, I present my math homework.

Note: My AIM screen name duoindrag is, as of now, in permanent invisible mode. So if it looks like I'm offline, that's why.

The class I am taking is linear algebra. These are the problems I'm working on today. For the most part, I am at a complete loss as to how to start (which is the part I always have the most trouble with).

(1) The vectors A1 = [1, 2]t and A2 = [2, -3]t are (obviously) independent in ℝ2. According to Theorem 2, they must therefore span ℝ2. As an example of this, choose some random non-zero vector B in ℝ2 and find constants x and y such that B = xA1 + yA2. Please do not choose either A1 or A2 as B. This is not "random"!

(3) Let A1 = [1, 2]t and A2 = [2, 4]t in ℝ2. Find a vector B in ℝ2 for which there are no constants x and y, such that B = xA1 + yA2. [Hint: Draw a picture.] Find another vector C such that x and y do exist. What geometric condition must C satisfy?

(4) "The vectors A1 = [1, 2]t and A2 = [2, -3]t, and A3 = [2, 4]t span ℝ2." True or false? Explain.

(5) Does the subspace W in Example 6 [[spanned by X1 = [1, 2, -3]t, X2 = [3, -7, 2]t]] contain Z = [9, -8, -5]t?

(6) Prove that the given sets are subspaces of ℝn for the appropriate n. Find spanning sets for these spaces and find at least two different bases for each space. Give the dimension of each space.
(a) S = {[a + b + 2c, 2a + b + 3c, a + b + 2c, a + 2b + 3c]t | a, b, c ∈ ℝ}
(b) S = {[a + 2c, 2a + b + 3c, a + b + c]t | a, b, c ∈ ℝ}
(c) S = {[a + b + 2c, 2a + b + 3c, a + b + c]t | a, b, c ∈ ℝ}

(10) What is the dimension of M(m, n)? Prove your answer.

(15) Prove that these vectors form a basis for ℝ3:
X1 = [2, -3, 1]t, X2 = [1, 2, 3]t, X3 = [7, -2, 4]t.

(26) Prove that the uniqueness theorem from Exercise 25 is false for spanning sets that are not bases. That is, suppose that {X1, X2, ..., Xn} spans a vector space V and is dependent. Prove that every element XV has at least two different expressions as a linear combination of the spanning vectors. It might help to consider first the case of X = 0.
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teruteruboozu From: teruteruboozu Date: Friday 17th September 2004 08.31 (UTC) (Link)
For someone who's in Math 25, your homework makes my brain explode several times over. But! *pulls Roy out and dresses him in a cheerleader uniform, complete with pompoms* Cheer her on, Roy! Cheer!

Roy: >\ *fries his mun*
makaioh From: makaioh Date: Friday 17th September 2004 09.11 (UTC) (Link)
I can do your math homework too.
But first, I'll do Kym's.

Actually, I have a major presentation due at like 9am. So, first, I'll do that. Then I'll do everybody's math homework. It'll be fun!
valamelmeo From: valamelmeo Date: Friday 17th September 2004 17.50 (UTC) (Link)
Or I can do her math homework so I can feel smrt. I need something like that.
valamelmeo From: valamelmeo Date: Friday 17th September 2004 17.20 (UTC) (Link)
Oooooh, cheerleader!Roy!!! See, when you put him in outfits you know he's going to hate, you have to make sure to take away his gloves. He can't fry you that way, and it's very cute to see him jumping up and down trying to reach them while you hold them over his head, especially in that little pleated skirt. Or so Hughes says. ^_~