i am following this guide: http://www.calpoly.edu/~brichert/teaching/oldclass/f2002217/handouts/goof.pdf
my question is to find the linaer transformation that adheres to
$T(1,1,1) = (1,1,1)$
$T(0,1,0) = (0,1,0)$
$T(1,0,2) = (1,0,1)$
my matrix looks like this:
$\begin{pmatrix} 1 & 1 & 1 & | &b_1\\ 0 & 1 & 0 & | & b_2 \\ 1 & 0 & 2 & | & b_3 \\ \end{pmatrix}$
after reduction it looks like this:
$\begin{pmatrix} 1 & 0 & 0 & | &2b_1 -2b_2 -b_3\\ 0 & 1 & 0 & | & b_2 \\ 0 & 0 & 1 & | & b_3 +b_2 -b_1 \\ \end{pmatrix}$
i am getting that:
$T(b_1,b_2,b_3) = (b_1-b_2,2b_1-b_2-b_3,b_1-b_2)$
this is not the actual solution, it should be $(b_1,b_2,b_1)$
what am i doing wrong, i believe i havent made any arithmetic errors
Your matrix must be:
$\begin{pmatrix} 1 & 0 & 1 & | &b_1\\ 1 & 1 & 0 & | & b_2 \\ 1 & 0 & 2 & | & b_3 \\ \end{pmatrix}$