Find the image of the `(-2,-7)` under the transformations (x,y) to `(x-2y,-3x+y).`

Explanation

Let `(x_(1),y_(1)` be the image of the point (x,y) under the given transormations, then
`{(x_(1)=x-2y=1.x+(-2).y),(y_(1)=-3x+y=(-3).x+1.y):}`
`rArr" " [(,x_(1)),(,y_(1))]=[(1,-2),(-3,1)][(,x),(,y)]`
`=[(1,-2),(-3,1)][(,-2),(,-7)][(-2+14),(6-7)]=[(,12),(,-1)]`
therefore, the required image is `(12,-1).`