Recent content by Lanthanum

Aha! I think I have it. Since T is a linear transformation, T(0)=0, and T(au+ bv+ cw)=aT(u)+bT(v)+cT(w)=0 Since there exists scalars, a, b, c, not all 0, such that the above equation is true, S` is linearly dependent. I can't believe I missed that even after ZioX's advice, guess I...

If you factor out the 2 and split the limit into two parts then you have; 2 lim t->0 (t/sint) - lim t->0 (t)

If p(t) is the linear relationship between the vectors in S, does that mean that T[p(t)] is the linear relationship between the vectors in S`? If so I guess that proves that S` is also linearly dependent since there exists the linear relationship T[p(t)] between its elements.

lim x->0 of sinx/x =1, so lim x->0 of 1/(sinx/x) is also 1, and 1/(sinx/x)=x/sinx, so lim x->0 of x/sinx = 1 from here just rearrange the equation.

Homework Statement Let T:\Re^{n}\rightarrow\Re^{m} and let S={u,v,w}\in\Re^{n}. If S is linearly dependent, show that {T(u), T(v), T(w)} is also linearly dependent. Homework Equations N/A The Attempt at a Solution Since S\in\Re^{n} then S`\in\Re^{m}. Not sure where to go from here

It's one of those proofs that's decievingly easy. Start by defining two general vectors; let a=<x1,y1> and b=<x2,y2> where x and y are real.

What you get in that case is a vector which is normal to both QR and the position vector of P. This is not the same as the normal to the plane containing QR and the point P. Sorry but I'm not sure what you mean here. Nvm, I just realized what Nvm means!

You need to find a vector normal to the plane. First find two vectors that lie allong the plane. ie. QR and RS; QR=<-5,-2,5> and RS=<10,4,-3> A vector normal to the plane (n) will be normal to both of these. so; n=<-5,-2,5>X<10,4,-3> =<-14,35,0> (you can divide this by 7 cos it will still...

Homework Statement Given that q is an eigenvalue of a square matrix A with corresponding eigenvector x, show that qk is an eigenvalue of Ak and x is a corresponding eigenvector. Homework Equations N/A The Attempt at a Solution I really haven't been able to get far, but; If x is an...