Linear mapping/Plane/Image and preimage/1/Exercise

We consider the linear mapping ${}\varphi \colon \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$ given by the matrix ${}{\begin{pmatrix}8&4\\5&9\end{pmatrix}}$.

1. Determine the image of the line defined by the equation

   ${}5x-7y=0\,.$

2. Determine the preimage of the line given by the equation

   ${}6x-11y=0\,.$

Create a solution