let L: R^2 - R^2 be defined by
L(x,y)= (x-2y,x+2y)
let s= {(1,-1),(0,1)} be a basis for R^2 and let T be the natural basis for R^2. find the matrix representing L with respect to
a) S b) S and T c) T and S d) T

Question

let L: R^2 -> R^2 be defined by 
L(x,y)= (x-2y,x+2y)
let s= {(1,-1),(0,1)} be a basis for R^2 and let T be the natural basis for R^2. find the matrix representing L with respect to
a) S  b) S and T  c) T and S  d) T

anonymous · Answer

@myininaya need help just tell me the procedure how to solve

anonymous · Answer

@ash2326 help

anonymous · Answer

I will tell you how to do a). The rest is similar
$$ L(1,-1)=\{3,-1\}=3
   \{1,-1\}+2 \{0,1\}\
L(0,1)=\{-2,2\}=-2 \{1,-1\}+0\{0,1\}\
M=\left(
\begin{array}{cc}
 3 & -2 \
 2 & 0 \
\end{array}
\right)
$$

anonymous · Answer

@eliassaab

anonymous · Answer

sir where this 3 came from ???

anonymous · Answer

Look at the first line.

anonymous · Answer

sorry sire but still not getting the point ... please a bit more explanation

anonymous · Answer

ok no i get it. its by simply putting values

anonymous · Answer

thanks sire really appreciate your help :)