Old 7th February 2005, 20:37   #1
dlinkwit27
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Woo Hoo for Proofs!

Let u1, u2,...,uk be vectors in Rn and c be a scalar. Prove that the span of {u1, u, ..., uk} is equal to the span of {u1+cu2, u2, ..., uk}.

NO! I DONT WANNA! This sucks

/edit
I think I may have it I hope so at least.

Last edited by dlinkwit27; 7th February 2005 at 21:00.
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Old 7th February 2005, 21:06   #2
mark
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sounds worse than integrating to find the area between two curves, using long division to factorize the cubic (my homework)...
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Old 7th February 2005, 21:07   #3
mysterious_w
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When I clicked on the link to this topic I'm sure it said

"Woohoo for poofs!"




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Old 7th February 2005, 21:11   #4
dlinkwit27
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nobby: that stuff is easy (now)
mysterious: sarsacim.

I think that this will do it, but I am not sure. I get to meet with a group on wed. to check it.

Let v be the vector u1+cu2. Vector v can also be written as a linear combination of u1, u2, …, uk with coefficients d such that d1=1, d2=c, and d3=d4=…=dk=0 such that:

v = d1u1+d2u2+d3u3+…dkuk = 1u1+cu2+0u3+…+0uk = u1+cu2


Thus, we can conclude that v belongs to Rn, thereby making the span of {u1, u2, …, uk} equal to the span of {u1+c*u2, u2, ..., uk} by Theorem 1.6 (c).
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Old 7th February 2005, 21:14   #5
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how old are you dlink? i'm 20 and i don't think i learned any of that stuff in high school. i'm good with math but i don't think that's what was taught in the classes i got.

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Old 7th February 2005, 21:19   #6
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I just turned 20. I'm in my 4th semester of colege/university and am in Elementary Lineral Algebra: A Matrix Approach.

Just to make it more fun, my professor wrote the book for this subject. Literally. It's nice sometimes, but if you dont understand the lectur or the book, you cant relaly refrence the other for clairity.
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Old 7th February 2005, 21:32   #7
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man, and I thought my maths was hard. Top set at school, and today we revised bearings.




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Old 7th February 2005, 21:37   #8
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Quote:
Originally posted by dlinkwit27
I just turned 20. I'm in my 4th semester of colege/university and am in Elementary Lineral Algebra: A Matrix Approach.
no wonder it didn't look familiar. i only got algebra when i was doing the college thing.

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Old 7th February 2005, 22:27   #9
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Quote:
Originally posted by mysterious_w
man, and I thought my maths was hard. Top set at school, and today we revised bearings.
i would kill for bearings...
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Old 7th February 2005, 22:51   #10
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remember logic proofs? I miss those. I'm in AP Calc AB. Senior year of high school.

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Old 7th February 2005, 23:56   #11
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wtf are bearings?
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Old 8th February 2005, 01:54   #12
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The logic is right in your proof. Basically its because u1+cu2 is a linear combination of u1...uk hence you haven't really changed the set your working with. (ie. you can regenerate any vector from u1..uk from a linear combination of u1+cu2, u2...uk)

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Old 8th February 2005, 02:55   #13
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2 + 2 = 5

The extent of my math skills.

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I stayed for the ballbag.
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Old 8th February 2005, 03:40   #14
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Quote:
Originally posted by Hollow
The logic is right in your proof. Basically its because u1+cu2 is a linear combination of u1...uk hence you haven't really changed the set your working with. (ie. you can regenerate any vector from u1..uk from a linear combination of u1+cu2, u2...uk)
awesome! thanks much for the conformation! What math are you in/do you teach?
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Old 8th February 2005, 05:57   #15
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ei dork!

looks like we have the same math teacher
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Old 8th February 2005, 09:15   #16
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Quote:
Originally posted by dlinkwit27
awesome! thanks much for the conformation! What math are you in/do you teach?
I'm currently dealing with a massive case of senioritis during the rundown to graduation. I'll have a B.S. in chemistry with a math minor come June. In the fall I'll be starting grad school at Cornell or Syracuse most likely.

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Old 8th February 2005, 13:36   #17
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Quote:
Originally posted by Hollow
I'm currently dealing with a massive case of senioritis during the rundown to graduation. I'll have a B.S. in chemistry with a math minor come June. In the fall I'll be starting grad school at Cornell or Syracuse most likely.
nice. Well congrats and making it that far. It's weird. The past 4 semesters have just flown by, and yet, it feels as if the next 6 are going to take forever to get through.
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