Suppose that we have a $2-$dimensional data set X$.$ We transform each data point Xj$=($Xj$,1,$Xj$,2)$ as follows: Xj~$=($aXj$,1$c$,$bXj$,2$c$),$ where a$,$ b$,$ c are constant values. This is a linear transformation, because our transformed data comes from simple operations that use 'first powers' of the original data.

If our given data set is linearly separable, does the same hold true for the transformed set? In the following cells you can plot a transformed version of the Iris dataset, so that you see how it behaves $($for your choice of a$,$ b$,$ c$.)$ But you should also try and justify your answer in a theoretical way: if there exists a 'good' perceptron for the original data set, what would be the weights for the perceptron that works on the transformed set? Are there any issues that might arise?