Select the correct true$/$false pair about the following two statements:

Support vector machines are able to produce non$-$linear decision boundaries by transforming low$-$dimensional inputs into high$-$dimensional space. This usually works because high$-$dimensional data is more likely to be linearly separated than low$-$dimensional data.

"Kernel trick" refers to first applying the above transformation and then computing the dot products between the transformed data points.

Both statements are true

Both statements are false

Statement $1$ is true, Statement $2$ is false

Statement $1$ is false, Statement $2$ is true