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

Flop21

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Re: MATH1231/1241/1251 SOS Thread

Oh so I think I'm close...

I keep getting down to x^2 y + y^3/3 + C... when the final answer is 3x^2 y + y^3 = A. What have they done between my step and the final answer?
 

InteGrand

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Re: MATH1231/1241/1251 SOS Thread

Oh so I think I'm close...

I keep getting down to x^2 y + y^3/3 + C... when the final answer is 3x^2 y + y^3 = A. What have they done between my step and the final answer?
 

Flop21

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Re: MATH1231/1241/1251 SOS Thread

Oh I missed you saying this.

OKAY GREAT.

Just got the next one after this one correct anyway, so I'm on the right track now.

Thank you.
 

InteGrand

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Re: MATH1231/1241/1251 SOS Thread

By definition T(0) = 0.
He was more asking about the other direction, i.e. whether he could conclude from T(something) = 0 that something = 0. This is guaranteed if and only if the linear map T is a one-to-one map. If T is not one-to-one, it'll have a non-trivial kernel.
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

I see, really nice :)

Is there a way to do it in a forwards manner though? Because I asked it for a friend and I'm not sure if, in their course, they need to consider the contrapositive

If it's probably too hard then maybe don't worry
 

InteGrand

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Re: MATH1231/1241/1251 SOS Thread

I see, really nice :)

Is there a way to do it in a forwards manner though? Because I asked it for a friend and I'm not sure if, in their course, they need to consider the contrapositive

If it's probably too hard then maybe don't worry
Not really, because to conclude just from T(something) = 0 that something = 0 (which is what you seemed to want to do), we'd have to know T was one-to-one, but T can be any linear map (and the result holds regardless). You'd end up having to do it by contradiction I think (which makes it similar to contrapositive).
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

Not really, because to conclude just from T(something) = 0 that something = 0 (which is what you seemed to want to do), we'd have to know T was one-to-one, but T can be any linear map (and the result holds regardless). You'd end up having to do it by contradiction I think (which makes it similar to contrapositive).
Fair enough, alright sweet no worries
 

Flop21

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Re: MATH1231/1241/1251 SOS Thread

Finding the basis for the kernel of this matrix (already row reduced):




The answers show (sorry you can barely see):




My understanding to solve this you make the non leading column = lambda, so e.g. x3 = lambda. Then you solve the equations.

But what happens when you have multiple non-leading columns like here? I don't understand what they've done in the answers, and why they have made two things = lamda, and one other = ,u.
 

Drsoccerball

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Re: MATH1231/1241/1251 SOS Thread

Finding the basis for the kernel of this matrix (already row reduced):




The answers show (sorry you can barely see):




My understanding to solve this you make the non leading column = lambda, so e.g. x3 = lambda. Then you solve the equations.

But what happens when you have multiple non-leading columns like here? I don't understand what they've done in the answers, and why they have made two things = lamda, and one other = ,u.
If you have two unknowns in an equation let one of them equal to a variable.
 

seanieg89

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Re: MATH1231/1241/1251 SOS Thread

Have they explicitly said you cannot argue by contrapositive/contradicition/etc? These are just fundamental methods of proof, not specific knowledge that may or may not be in syllabus.

Your lecturer might not specifically mention them but I would be extremely surprised if you are not allowed to use them. Sometimes proofs are just more concise etc when structured in this way.
 

He-Mann

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Drsoccerball

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Re: MATH1231/1241/1251 SOS Thread

Have they explicitly said you cannot argue by contrapositive/contradicition/etc? These are just fundamental methods of proof, not specific knowledge that may or may not be in syllabus.

Your lecturer might not specifically mention them but I would be extremely surprised if you are not allowed to use them. Sometimes proofs are just more concise etc when structured in this way.
It may just be unfair that we know a method some normal maths students wouldn't know but let's not take the risk.
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

Have they explicitly said you cannot argue by contrapositive/contradicition/etc? These are just fundamental methods of proof, not specific knowledge that may or may not be in syllabus.

Your lecturer might not specifically mention them but I would be extremely surprised if you are not allowed to use them. Sometimes proofs are just more concise etc when structured in this way.
Nah they're definitely allowed. It's only the unfairness factor in that not everyone would think in that direction due to zero exposure to it.
 

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