Thank you. Question has been solved =] You were a great help.
Edit: Crap, it won't let me edit the title or first post to say that it's been solved. :(
Darn.. I feel sooo lost but I'm starting to have an idea of what is happening
I'll start here again:
(cos kx2, kx1*(kx2)3) is the end point, because from here I cannot isolate k to prove the definition of linearity.
So to show a counter example, can I just substitute in any number other than 1...
I see.
So a few notes to keep in mind:
Domain -> Columns of original function
Codomain -> Columns of mapped (if I'm even using the right terminology)
So would ii be:
g(x1, x2) = (cos x2, x1x23)
Domain: R2
Codomain: R2
And
g(k(x1, x2))
= g(kx1, kx2)
= (cos kx2, kx1x23) (Am I supposed...
Ah thank you. I'm still reaally confused and it's making me so frustrated. I've been working at the same question for 5 hours.. but at least I can give you guys a better picture of where I'm at now. So you're saying that I should be able to show f(kx) = kf(x), if it is linear.
I've learned...
Crap, I'm really sorry, I completely messed up part ii.
ii was supposed to say g(x1, x2) = (cos x2, x1x2^3) It's hard to see, but what the right side says is cosine of xsubscript2, xsubscript1xsubscript 2, to the exponent 3.
Thanks for your example! Based on that, I'm guessing that I can do...
Homework Statement
For the following mappings, state the domain and the codomain. Determine whether the mapping is linear by using the definition of linearity: either prove it is linear or give a counterexample to show why it cannot be linear.
i.) f(x1,x2,x3)=(2x2, x1−x3)
ii.) g(x1, x2) =...
Sorry for double posting - for some reason my browser isn't letting me click edit on my last post :(
When finding the direction of the force applied, could I use sine law?
Ex:
6.77N is the magnitude of the change of momentum, thus it would represent the hypotenuse of a right angle triangle...
22.4 N would be the magnitude of the change of momentum, if I were to divide this by time I would get
22.4 / 3.31s
= 6.77 N
Oh, right! That makes perfect sense all the sudden, a bit more reading had me discover that momentum is in Newton seconds, so if I divided by time, seconds would...
Ah, momentum, brings back memories.
So then:
Px(initial) = mass of object * initial velocity
= 1.2kg(14.4m/s)
= 17.28
Px(final) = mass of object * x component final velocity
= 1.2kg(23.88m/s)
= 28.656
Py(final) = mass of object...
First post =]
Requesting guidance with this particular problem:
Homework Statement
A 1.20 kg object is moving in the x direction at 14.4 m/s. Just 3.31 s later, it is moving at 28.8 m/s at 34.0 degrees to the x axis.
a.) What is the magnitude of the force applied during this time...