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#1 2012-10-05 03:03:16

Deon588
Member
Registered: 2011-05-02
Posts: 68

Linear algebra: intersection

Hi all I recently started linear algebra and my prescribed book seems to require some 3-dimensional geometry knowledge which i've never touched...  Any idea how to go about this?
Let L be the line that passes through the points P(2,4,-1) and Q(5,0,7) Determine the point of intersection of L and the x-y plane
Should the z-coordinate be 0 because the question only mentions the x-y plane?
Thanks

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#2 2012-10-05 08:07:00

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Linear algebra: intersection

hi Deon588

Yes, z = 0 will do it.

Do you know how to get the vector equation of a straight line.

If no, you could have a look at

http://www.mathisfunforum.com/viewtopic … 57#p159557

or post back.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-10-06 03:23:08

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Linear algebra: intersection

Hi Bob!!!
Good to know you're still on these forums, I remember you helped me get past a lot of challenging problems last year.
I think so, is this the way to do this?  Sorry for the bad notation i'll have to go over the LaTeX post again...
x=p+t(q-p)
(x,y,z)=(2,4,-1)+t((5,0,7)-(2,4,-1))
(x,y,z)=(2,4,-1)+t(3,-4,8)
x=2+3t
y=4-4t
(x,y)=(2+3t,4-4t)
Thanks a lot

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#4 2012-10-06 03:24:09

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Linear algebra: intersection

the emoticon is supposed to be =

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#5 2012-10-06 05:10:53

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Linear algebra: intersection

hi Deon588

Yes, you have done that well!  smile  (This emoticon is meant to be there!)

will do nicely.

so you have

x = 2 + 3t
y = 4 - 4t

and
z = -1 + 8t

Don't ignore the z component ... rather make it equal to zero

0 = -1 +8t

solve for t

That fixes the value of t and so you can put back into the x and y equations to get the point as three numbers.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2012-10-06 05:57:28

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Linear algebra: intersection

Thanks again that totally clears it up for me.
I have another question for you:)  I recently lost a month of studying because of medical issues...  The only part of Linear algebra I haven't covered is the chapter dealing with eiggen values (not sure if I spelled that correctly) I see that some complex number skills are required for that chapter and i've never done complex numbers before.  I went through the past 3 years exam papers of my university and it seems like eigen vallues rarely appears and if it does it counts maybe 7/100 marks.  i'm writing Linear algebra on 23/10 so not much time left.  So right now i'm not sure at all whether just to forget about the eigen values and focus on the other work or try to learn some basic complex number theory and do the eigen value chapter as I have 4 other subjects this semester...  What would you recommend I do?  would it be possible to learn enough about complex numbers to use in a elementary linear algebra course?
Thanks

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#7 2012-10-06 20:33:58

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Linear algebra: intersection

hi Deon588

That's a tough question.  I'd hate to give the 'wrong' answer.

Would you be able to post a question or two so I can see what sort of thing they're asking?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2012-10-06 21:28:16

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Linear algebra: intersection

Hi Bob
Yes of course I attached 3 questions
Thanks

View Image: complex number problems.gif

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#9 2012-10-07 02:46:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Linear algebra: intersection

hi Deon588

Ok, that's a relief for me.  I had thought I might be given questions beyond my knowledge ... then I'd have been in trouble.  But these look OK although I cannot see my way to the end of Q3.  I'll have to write stuff down.

EDIT:  Actually I can see it comes from the same theorem as Q2. so Q3 is ok too.

But these are just basic complex theory, not eigenvectors.  So do you have basic complex on the exam or is it just during linear algebra, eigenvectors; in which case I'd still like to see a question on that.  On the basis of what I've seen and you have said about the time factor, it seems you could take the risk and leave out eigenvectors.  But, please don't blame me if lots come up.  Don't forget, you're the one looking at the past papers.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2012-10-07 23:09:04

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Linear algebra: intersection

Hi Bob
I made a big mistake, I have a newer edition of the prescribed book which has a chapter on eigen values added.  I just checked on my study guide and see it's only the basic complex number theory that I need to study
Thanks for taking a look at it anyhow
Deon

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#11 2012-10-08 03:03:03

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Linear algebra: intersection

hi Deon588,

That's OK.  The questions you posted don't look too bad so if you want to do the theory I'm here to help if needed.

http://www.mathsisfun.com/numbers/complex-numbers.html

http://en.wikipedia.org/wiki/De_Moivre's_formula

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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