Mathematics - 24 November 2007

cubic route (108)

2007-11-24 09:27:50 · 3 answers · asked by Im Juzt Meh 2

let V be a finite dimensional vector space, M and N linear subspaces of V, prove

dimM+dimN = dim(M+N) + dim(M n N)

n = intersection,


proof:
First prove the lemma
If U is a subspace of V and {u_1,..., u_k} is a base in U then there are some vectors v_1,..., v_l such that {u_1,..., u_k, v_1,..., v_l} is a base in V.

Now choose the base B in M n N. Extend it by lemma to a base Bm in M, and base Bn in N. Now prove that Bm u Bn is a base of M+N.

Let #X be a number of elements in X.
You have
dim M = #Bm
dim N = #Bn
dim (M+N) = #(Bm u Bn)
dim (M n N) = #B
and #(Bm u Bn) = #Bm + #Bn - #(Bm n Bn) = #Bm + #Bn - #B because Bm n Bn = B



does that look right, any help is appreciated

2007-11-24 09:08:20 · 3 answers · asked by Anonymous

I have a problem dealing with ring isomorphism.

My question can be seen in better detail at the link below at Cramster.com:

http://answerboard.cramster.com/math-topic-5-146838-0.aspx

2007-11-24 09:01:36 · 2 answers · asked by Anonymous

2007-11-24 08:53:49 · 6 answers · asked by Krystoffer W 1

Do You remember the old problem about the equilateral triangle on the rails? Given are 3 co-planar parallel lines, the distance between 1st and 2nd is a, between 2nd and 3rd - b (and a + b between 1st and 3rd of course).
Please follow the link below to see a picture:

http://i219.photobucket.com/albums/cc101/Andrey_Dyukmedzhiev/2D3D.gif

Easily follows that for all a ≥ 0 and b ≥ 0 there exists an equilateral triangle, having one vertex on each line with side length:
(2/√3)*√(a² + ab + b²)

Now the 3D analog: imagine 4 parallel planes at distances a, b and c between them. Does a regular tetrahedron exist, having one vertex on each plane? If so, find its edge length.

2007-11-24 08:53:43 · 1 answers · asked by Duke 7

write the rational expression in lowest terms

3q²-4qz+z²
---------------
q²-2qz+z²

2007-11-24 08:47:06 · 7 answers · asked by Jen1289 1

there are 2820 cars in farmington. the ratio of intermediates to compacts is 7:5 and the ratio of compacts to full-size cars is 8:9. how many full-size cars are there?

2007-11-24 08:45:20 · 2 answers · asked by karenmp1993 2

factor completely

12x^3-3xy^2

2007-11-24 08:44:27 · 4 answers · asked by crazy4u 1

2007-11-24 08:38:47 · 5 answers · asked by Hugh B 1

2007-11-24 08:17:55 · 4 answers · asked by kayy♥ 3

can u give work out so i can see how you reach to answers

I dont want to give my fractions as want to work out myself

but have 3 different fractions.. and how do i use the answer after finding the ratio thus gained to divide??

hope this makes sense

2007-11-24 08:16:01 · 5 answers · asked by Anonymous

A sector with central angle X is cut from a circle of radius 4 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of X such that the volume of the cone is a maximum.

Please help me and show all your work. I have no clue how to do this. Thank you! =)

2007-11-24 08:03:04 · 3 answers · asked by laweezer08 1

factor and solve.

3x^2+x-10=0

2007-11-24 07:59:20 · 3 answers · asked by God Bless America!~ 4

factor completely.

5a^2-125

2007-11-24 07:58:32 · 5 answers · asked by God Bless America!~ 4

Say our general eigenvector for the eigenpolynomial (x-2)(x-1)^4 is: (a+b, a-2b, ....)

We know
v1 = u1
and
v1 . v2 = 0

so I set up the equation
v1 = (a + b)
v2 = (a - 2b) - ((a-2b) (dotted into) (a+b) )/ ((a-2b) (dotted into) (a-2b) ) * (a-2b)

The v2 I got was (6ab^2 - 12b^3) / (a^2 + 4b^2)

multiply by the denominator i got
v2 = 6ab^2 - 12b^3

However, my v1 . v2 doesnt equal to zero.

Is this the right way to do it? or am i doing something wrong?

2007-11-24 07:57:42 · 1 answers · asked by elan_longterm_invest 2

Factor:

ax-bx+5a-5b





thank you

2007-11-24 07:56:53 · 4 answers · asked by Anonymous

Okay, for a mini project I created a (0,5),(3,1), (8,9) triangle.

Now I have to find the linear equation that corresponds to each side. How do I go about finding this..I would appreciate it if someone can teach me in doing 1 example.

Thanks.

2007-11-24 07:41:54 · 4 answers · asked by Anonymous

a=angle
no calculators please

2007-11-24 07:29:26 · 5 answers · asked by chrys 1

So my math teacher mentioned in class the other day in passing that if function f is both even AND odd then it must bue the zero function. He didn't really explain it though and it doesn't make a ton of sense to me. Is this true? If it is, can you provide a short proof that explains why it works for ALL functions f and not just a few examples?

2007-11-24 07:24:28 · 2 answers · asked by George Washington 2

he's telling me that if functions f and g are both odd, then so is f(g) f+g and f X g.
Can anyone prove or disprove this so that I can decide wether or not to put money on this bet. Thanks

2007-11-24 07:22:39 · 2 answers · asked by In Testimony Whereof 3

if V and W are finite dimensional vector spaces, prove that L(V,W) is isomorphic to L(W,V)

dont look for a mapping L(V,W) -->L(W,V)

2007-11-24 07:19:14 · 1 answers · asked by Anonymous

my grade nine D=RT problem:
a jet flew from Toronto to Paris at 800 km/h and returned at 700km/h. if the total trip, not including stopover time, took 15 h, how far is it from Toronto to Paris.
I need help forming the actual algebraic expression
i don't need the answer just help with the theory
usually, it's "if a jet took 10 hours, at 100 km/h, how far did it go", but this is different and i'm EXTREMELY unsure on how to solve it

2007-11-24 07:11:37 · 2 answers · asked by Ana B 2

how to take 0.6814 to percentage expression?

2007-11-24 07:10:59 · 5 answers · asked by Anonymous

the new Mario game is regularly priced at $39.99. it is on sale for 15% off. what is the sale price?

how do u find out? the sale price and discount

please give me notes on how to figure them out please

2007-11-24 07:05:33 · 5 answers · asked by Anonymous

2007-11-24 06:50:55 · 11 answers · asked by Katie 2

Can somebody help me solve this? I can't just use my calculator. Could you be so kind as to show me the steps.

log X + log (X + 15) = 2

2007-11-24 06:50:33 · 2 answers · asked by John 1

Case 1: (15) (15)=225
Case 2: (25) (25)=625
Case 3: (35) (35)=1225
Case 4: (45) (45)=2025
Case 5: (55) (55)=3025
Case 6: (65) (65)=4225
Case 7: (75) (75)=5625
Case 8: (85) (85)=7225
Case 9: (95) (95)=9025

2007-11-24 06:47:00 · 7 answers · asked by love 1

One poll found that 34% of male voters will support a candidate while another found that 42% of female voters will be in support. To test whether this candidate has equal support levels between male and female voters, what is the alternate hypothesis?

2007-11-24 06:32:22 · 3 answers · asked by Anonymous

Can someone help me find the derivative of

y=[ln(x^2)]^2

An answer is nice, but an explanation is better

2007-11-24 06:28:39 · 4 answers · asked by Liz 4

2007-11-24 06:26:01 · 3 answers · asked by bob 1