Question

Let T be a linear transformation from R^3 with respect to B_1 to R^3 with respect to B_2 defined by T([x,y,z]= [x+y, y-z, x+z]. Find u such that T(u)=w. I have tried using the transformation matrix I cannot invert to find u. Pretty confused now. Any help is greatly appreciated.

Answer 1

the transformation matrix T is defined by \[\left[\begin{matrix}1 & 1 & 0\\ 0 & 1 & -1\\1 & 0 & 1\end{matrix}\right]\]

Answer 2

find T^-1 , then plug into T^-1*W = U