$($a$)$ Compute the PCA and LDA $1$D projections for the following $2$D dataset:

Samples for class $1({}_1)$:$x_1=(x_1,x_2)=\{(4,2),(2,4),(2,3),(3,6),(4,4)\}$

Samples for class $2({}_2)$:$x_2=(x_1,x_2)=\{(6,8),(9,5),(8,7),(10,8)\}$

Draw the two principal components on the plot for PCA as vectors, as well as the projected blue and red points in $1D.$

Draw the projected $1$D data using LDA.

$($b$)$ Repeat $($a$)$ for the following dataset:

Samples for class $1({}_1)$:$x_1=(x_1,x_2)=\{(6,8),(2,4),(2,3),(3,6)\}$

Samples for class $2({}_2)$:$x_2=(x_1,x_2)=\{(9,5),(8,7),(10,8),(4,2),(4,4)\}$

$($c$)$ Comment and compare how good the $1$D projected data in $($a$)$ and $($b$)$ can be classified after PCA and LDA.

Write the code in PYTHON. You can use the information in the "Hands$-$On Machine Learning with Scikit$-$Learn, Keras, and TensorFlow, $3$rd Edition" book.