• Help the next generation of students in the community for the new syllabus!
    Share your notes and exam papers on our Notes & Resources page
  • We are looking for new moderators to join the Bored of Studies team!
    Click here for details

First Year Mathematics B (Integration, Series, Discrete Maths & Modelling) (1 Viewer)

Flop21

Well-Known Member
Joined
May 12, 2013
Messages
2,842
Gender
Female
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

why are you still doing matricies
I believe this topic is called "linear combinations and spans" or the overall topic is "vector spaces".
 

turntaker

Well-Known Member
Joined
May 29, 2013
Messages
3,944
Gender
Undisclosed
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

are you doing things like intersection of lines, planes etc
 

Flop21

Well-Known Member
Joined
May 12, 2013
Messages
2,842
Gender
Female
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

are you doing things like intersection of lines, planes etc
we're doing things like vector spaces (e.g. show that the set is vector space), subspaces (e.g. show that the line segment defined by blah is not a subspace of R3 or find distinct members of the set blah). And I guess we are coming to a point involving matrices in sets or subspaces or whatever.

Soz don't really know wtf I'm talking about at this point lol.
 

turntaker

Well-Known Member
Joined
May 29, 2013
Messages
3,944
Gender
Undisclosed
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

we're doing things like vector spaces (e.g. show that the set is vector space), subspaces (e.g. show that the line segment defined by blah is not a subspace of R3 or find distinct members of the set blah). And I guess we are coming to a point involving matrices in sets or subspaces or whatever.

Soz don't really know wtf I'm talking about at this point lol.
Nvm I was thinking about vectors not matricies. But the two are connected somehow.
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,104
Gender
Male
HSC
N/A
Re: MATH1231/1241/1251 SOS Thread

I'm stuck on a similar one :(

How do I find this vector???

You essentially have two conditions:

x -(1/4)y + 0z = 0

and

0x -(3/4)y + z = 0

(assuming your answer was right, I didn't check it).

So the vector (x,y,z) is in the column space of A iff it satisfies those two conditions.

You can turn those conditions into a matrix and get it into row-echelon form (actually in this case, it already is in row-echelon form).

Then do the usual procedure of setting a non-leading column's variable to a free parameter (in this case, that variable is z, so set z = lambda say), then use back substitution as usual to get x and y in terms of lambda.

This will mean you'll end up with x, y, z in terms of lambda, which means you can get a vector b as desired. For the sake of example, if you ended up with x = 2lambda, y = -lambda, z = lambda, we'd have (x,y,z) = (2lambda, -lambda, lambda) = lambda (2,-1,1), and thus a vector we could choose for b would be (2,-1,1).
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

Nvm I was thinking about vectors not matricies. But the two are connected somehow.
In a way a matrix is just a ton of vectors smacked side by side
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

Am I doing something wrong with algebra or do I actually need to go for partial fractions? (Please don't complete the question)



 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,104
Gender
Male
HSC
N/A
Re: MATH1231/1241/1251 SOS Thread

Am I doing something wrong with algebra or do I actually need to go for partial fractions? (Please don't complete the question)



I think you made a simplification error in getting the second last line.
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

I think you made a simplification error in getting the second last line.
Oh my bad I dropped a negative in that line which I later reintroduced. But wait

Factoring -v out I have

1 + 2/(1+v^2) = (1+v^2+2)/(1+v^2) = (3+v^2)/(1+v^2) right?


Sent from my iPhone using Tapatalk
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,104
Gender
Male
HSC
N/A
Re: MATH1231/1241/1251 SOS Thread

Oh my bad I dropped a negative in that line which I later reintroduced. But wait

Factoring -v out I have

1 + 2/(1+v^2) = (1+v^2+2)/(1+v^2) = (3+v^2)/(1+v^2) right?


Sent from my iPhone using Tapatalk
Correct!
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

:)

But then.. Damn so I do have to p.f. it don't I haha


Sent from my iPhone using Tapatalk
 

Flop21

Well-Known Member
Joined
May 12, 2013
Messages
2,842
Gender
Female
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

I've got a formula here for the normal vector to the surface:

<Fx(xo,yo), Fy(xo,yo), -1>

but then somewhere else I see them using this:

<-Fx(xo,yo), -Fy(xo,yo), 1>

Which one is correct?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,104
Gender
Male
HSC
N/A
Re: MATH1231/1241/1251 SOS Thread

I've got a formula here for the normal vector to the surface:

<Fx(xo,yo), Fy(xo,yo), -1>

but then somewhere else I see them using this:

<-Fx(xo,yo), -Fy(xo,yo), 1>

Which one is correct?
We can use either for the normal, because those two vectors you've written are just negatives of each other, which means they are both valid normals (remember, two vectors that are just multiples of each other will both be valid direction vectors for a line).
 

Flop21

Well-Known Member
Joined
May 12, 2013
Messages
2,842
Gender
Female
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

I'm not sure what they want me to enter here. All results I get decimals, after finding the derivative of that integral.

 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

A bit lost in how to incorporate the nominal rate here. Need help with setting up the relevant ODE. I have a formula to find the effective rate for continuous compounding but it's taught in ACTL and not MATH.

 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,104
Gender
Male
HSC
N/A
Re: MATH1231/1241/1251 SOS Thread

A bit lost in how to incorporate the nominal rate here. Need help with setting up the relevant ODE. I have a formula to find the effective rate for continuous compounding but it's taught in ACTL and not MATH.

 
Last edited:

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,807
Gender
Male
HSC
2015
Re: MATH1231/1241/1251 SOS Thread

Lol they made us solve this differential equation by considering how it is an exact ODE. But the solution y=Ax just bugs me... is there a shorter way to doing this one haha

 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top