HW February 5
For the homework due on Feb.5, i am not understanding how to do it. On 44 and 48, i just don't know where to start out at. Any hints???
on 44 its asking if v x x can be written as a linear transformation using the components of v in its matrix A. Basically youre looking to see if the vector
can be written as [(v2)(x3)-(v3)(x2) [a [d [g (v3)(x1)-(v1)(x3) (x1) * b + (x2) * e + (x3) * h (v1)(x2)-(v2)(x1)] c] f] i]
where (x1), (v1), (x2), etc are 1st, 2nd, and 3rd components of the vectors v and x and variables a-i are constants in terms of the components of the vector v. for example a=0 b=(v3) and c=-(v2) On 48 just come up with two 2x2 matrices to represent L and T with variables and multiply them by 2 vectors with variables as components. If the formulas you get can be made independent of the components of the vectors (ie you can eliminate those variables from all equations by substitution or other means) then youll get L and Ts components to have some relationship independent of the vectors youre multiplying them by. youll find that their components must be equal --Rmcclur 12:17, 5 February 2010 (UTC)
