Class Activity: Data balancing with SMOTE

For the following data points

$x=(1,1),x_n=(3,2)$

and for $=0\mathrm{.}6$ add a new data point.

Class Activity: Dimensionality reduction

For the following training dataset:

What is the minimum dimensionality?

How do you get to that minimum dimensionality?

Is PCA able to get this minimum dimensionality? If Yes, how? $IfNo,$ Why