Using any mnist data set, run LDA on the dataset. Remember LDA is a supervised model so partition the dataset to $80\%$ in the training set and $20\%$ in the testing set. Then plot the data with a scatter plot in Python. Then with this same dataset answer if it's possible to project the LDA data in $3$ dimensional space. Explain why or why not. With the plot ensure that it has proper legend, x coord name, y coord name, and each object seperately colored. Share the code, the plot and the explanation.