Recent content by lo2

Ok thanks for the help! :)

Just came to think of something: I have expanded a1, a2, and a3 to a basis for R^5 by adding e1 = (1,0,0,0,0) and e2 = (0,1,0,0,0). So since they are in this basis they have to be linear independent of a1, a2 and a3 right? And hence e1 and e2 do not lie in the span of a1, a2 and a3?

No I just have to come up with a vector in R^5 that does not lie in span(a1, a2, a3).

Homework Statement I have this span, spanned by these three vectors in R^5: \underline{a_1}= \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 4 \\ 0 \end{array} \right) \underline{a_2}= \left( \begin{array}{c} 1 \\ -1 \\ 2 \\ 4 \\ 3 \end{array} \right) \underline{a_3}=...

Homework Statement Well as I said what is the chance of getting at most one six when rolling two dice twenty times? Homework Equations I know the probability of getting one six in one roll with two dice is: 11/36 And not getting one is: 25/36 The Attempt at a Solution...

Ah yeah ok, thanks a lot for the help! :)

Ok well I am not exactly sure what you mean here, but if you are asking what it is I need to show then it is: I have this general homogeneous function, which is a C^1 function: f(tx,ty)=t^k f(x,y) And then I have to show that this function satisfies this Euler equation...

Ok well I kind of have to go soon, so if you would please have a short glance at my suggested solution, I would be more than happy!

Ok I think I have got something: If we first differentiate f(tx,ty) We get: x\frac{\partial f}{\partial xt}(xt,yt)+y\frac{\partial f}{\partial yt}(xt,yt) And since this has to be equal to k\cdot f(x,y) We have that t^k Can only be a constant when t=1, so if we do that we get...

Well I must admit that I am still not sure how to compute that. As you do not know what the function is, and thereby I find it hard differentiate...

I do not want to seem rude. But might someone else perhaps chip in with a little bit of help? Would be most appreciated! :)

Well I guess not, I am not sure what this differentiates up to be: \frac{\partial f}{\partial tx}(tx,ty) The other one I think I got correct? \frac{\partial f}{\partial t}(tx) = x

Ok so I get this when I differentiate f(xt,yt): \frac{\partial f}{\partial t}(xt,yt) = 1\cdot x + 1\cdot y = x + y But I am not sure how to differentiate: t^k f(x,y) Shall I once again differentiate with regards to t?

But I have this equation: x\frac{\partial f}{\partial x}(x,y)+y\frac{\partial f}{\partial y}(x,y)=k\cdot f(x,y) Where I have to differentiate first with regards to x and then y. So am I not sure I can see how I should just differentiate with regards to t.

Homework Statement Ok I have this general homogeneous function, which is a C^1 function: f(tx,ty)=t^k f(x,y) And then I have to show that this function satisfies this Euler equation: x\frac{\partial f}{\partial x}(x,y)+y\frac{\partial f}{\partial y}(x,y)=k\cdot f(x,y) Homework...