$($a$)$ For this problem of performing PCA on countries by treating each country$$s food consump$-$ tion as their $$feature$$ vectors, explain how the data matrix is set$-$up in this case $($e$.$g$.,$ the columns and the rows of the matrix correspond to what$).$ Now extract the first two principal components for each data point $($thus$,$ this means we will represent each data point using a two$-$dimensional vector$).$ Draw a scatter plot of two$-$dimensional representations of the countries using their two principal components. Mark thecountries on the plot $($you can do this by hand if you want$).$ Please explain any pattern you observe in the scatter plot.

$($a$)(10$ points$)$ Now, we will perform PCA analysis on the data by treating country consumptions as $$feature$$ vectors for each fooditem. In other words, we will now find weight vectors to combine country consumptions for each food item to perform PCA another way. Project data to obtain their two principle components $($thus$,$ again each data point $$ for each food item $$ can berepresented using a two$-$dimensional vector$).$ Draw a scatter plot of food items. Mark the food items on the plot $($you can do this byhand if you want$).$ Please explain any pattern you observe in the scatter plot.