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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: /0 on January 28, 2008, 07:40:20 pm

Title: Just a quickie (parameters)
Post by: /0 on January 28, 2008, 07:40:20 pm: Is $\{ (x,y,z): (\lambda, \ 3\lambda,\ 8\lambda ), \lambda \in \Re\}$ the same as $\{ (x,y,z): \left(\frac{\lambda}{2},\ \frac{3\lambda}{2}, \ \frac{8\lambda}{2}\right), \ \lambda \in \Re \}$ or $\{(x,y,z): (\lambda + 10, 3\lambda +10, 8\lambda + 10), \lambda \in \Re \}$ ?

Is this ok for other operations too?

Just checking lols, thanks
Title: Re: Just a quickie (parameters)
Post by: humph on January 29, 2008, 10:46:51 am: yeah, they're all the same.

also (being nitpicky :P ) use $\mathbb{R}$ for the reals, $\Re$ is supposed to be for the real part of a complex number. different meanings completely...
Title: Re: Just a quickie (parameters)
Post by: Collin Li on January 29, 2008, 11:03:24 am: How do you use $\Re$ ? If I wanted to refer the real part of $w = 3i + 2$ for example.
Title: Re: Just a quickie (parameters)
Post by: humph on January 29, 2008, 11:07:24 am: Quote from: coblin on January 29, 2008, 11:03:24 am
How do you use $\Re$ ? If I wanted to refer the real part of $w = 3i + 2$ for example.
$\Re (w) = 2$ and $\Im (w) = 3$ , for example. you could also use it to signify the real part of a complex function, or something along those lines.
Title: Re: Just a quickie (parameters)
Post by: /0 on January 29, 2008, 01:57:31 pm: Thanks humphdogg
Title: Re: Just a quickie (parameters)
Post by: Ahmad on January 29, 2008, 08:58:59 pm: The ordered triple (10,10,10) resides in the last set (by taking lambda = 0), but does it reside in the first two?
Title: Re: Just a quickie (parameters)
Post by: /0 on January 29, 2008, 10:21:15 pm: Lol...thanks, Ahmad, right as usual :D. I was wondering why I kept getting the answer wrong, since in one question I changed

$\{(x,y,z,w):(\lambda +8, \ \lambda, \ \frac{-4\lambda-6}{3}, \ \frac{-6-2\lambda}{3})\}$ to

$\{(x,y,z,w): (3\lambda + 24, \ 3 \lambda, \ -4\lambda - 6, \ -6-2\lambda)\}$

just so its easier to write in that 8 mm line spacing. It's hard to notice how it's wrong :( but I guess it is.

I would have thought you could multiply everything by an integer and still keep it equivalent.
Title: Re: Just a quickie (parameters)
Post by: Mao on January 30, 2008, 06:25:18 pm: DivideBy0 is that for methods CAS??? i never learnt any of that stuph.....
Title: Re: Just a quickie (parameters)
Post by: /0 on January 30, 2008, 07:33:23 pm: Um it's a chapter in Essential Maths Methods, but I don't think it's necessary to the course. Dunno why they put it in there really :/
Title: Re: Just a quickie (parameters)
Post by: Neobeo on January 31, 2008, 10:07:58 am: Quote from: DivideBy0 on January 29, 2008, 10:21:15 pm
Lol...thanks, Ahmad, right as usual :D. I was wondering why I kept getting the answer wrong, since in one question I changed

$\{(x,y,z,w):(\lambda +8, \ \lambda, \ \frac{-4\lambda-6}{3}, \ \frac{-6-2\lambda}{3})\}$ to

$\{(x,y,z,w): (3\lambda + 24, \ 3 \lambda, \ -4\lambda - 6, \ -6-2\lambda)\}$

just so its easier to write in that 8 mm line spacing. It's hard to notice how it's wrong :( but I guess it is.

I would have thought you could multiply everything by an integer and still keep it equivalent.

If you insist on removing all fractions, you could for example let $\theta=\frac{\lambda}{3}$
in which case in would simplify to
$\{(x,y,z,w):(3\theta +8, \ 3\theta, \ -4\theta-2, \ -2-2\theta)\}$