## annas Group Title 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 2 years ago 2 years ago

1. annas Group Title

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

2. annas Group Title

@ash2326 help

3. eliassaab Group Title

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

4. annas Group Title

@eliassaab

5. annas Group Title

sir where this 3 came from ???

6. eliassaab Group Title

Look at the first line.

7. annas Group Title

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

8. annas Group Title

ok no i get it. its by simply putting values

9. annas Group Title

thanks sire really appreciate your help :)