Prove or Disprove the following statements either true or false using mathematical equation.

K-means MC Question 7 of 10 (8 Points) Answered In general (i.e., no matter with which input data we start the algorithm), it holds that... If the set of data points is linearly independent, it is not possible that the k-means algorithm returns two nonempty clusters with the same mean. If the first data point is initially assigned to the first cluster, the k-means algorithm returns a global minimum of the cluster energy function. If the first data point is initially equal to the first cluster mean, the k-means algorithm returns a local minimum of the cluster energy function. The k-means-algorithm returns a clustering with exactly k nonempty clusters