GRST 425 Lecture 3: Knowledge about Britain.pdf

Suppose V and W are finite dimensional vector spaces where beta = {v rightarrow 1,..., v rightarrow n} is a basis for V. Prove that if T : V rightarrow W and U : V rightarrow W are linear maps such that T(v rightarrow i) = U(v rightarrow i) for all 1 le i le n then T = U. Hint : Use linearity!

Given the acceleration vector A(t) = t2 i - 2 j + e3t k, and the initial position R(0) = 2i+j - k and velocity V(0)= i - j - 2 k, find (A) the velocity and (B) the position vector at time t. V(t) = i + j + k R(t) = i + j + k

Let u(t)=2ti+sin tj-cos tk and v(t) = I + t^2j - tk. Compute each of the following: d/dt(u(t).v(t)) d/dt(u(t) x v(t))