The transformation B\displaystyle {B} from R2\displaystyle \mathbb{R}^{{2}} to R2\displaystyle \mathbb{R}^{{2}} first projects onto the y\displaystyle {y}-axis and then scales the x\displaystyle {x}-component by 5\displaystyle -{5}. Find the matrix for this transformation, according to the standard basis vectors.

Answer: B=\displaystyle {B}=
 
 
 

The transformation G\displaystyle {G} from R2\displaystyle \mathbb{R}^{{2}} to R2\displaystyle \mathbb{R}^{{2}} performs those steps in reverse order. First it scales the x\displaystyle {x}-component by 5\displaystyle -{5} and then projects onto the y\displaystyle {y}-axis. Find the matrix for this transformation, according to the standard basis vectors.

Answer: G=\displaystyle {G}=