Question $3-$ PCA $[10$ pts$.]$

Define $v_1$ and $v_2$ as the directions of the first and second principal component, with $||v_1||=||v_2||=1,$ meaning they are vectors of size $1.$

$[5$ pts$.]$ Sketch the figure below and label $v_1$ and $v_2$ on the the figure. The arrows should originate from the mean of the distribution. You do not need to solve numerically, instead visually estimate the directions.

$[5$ pts$.]$ Sketch where the points A and B will be when projected on the dimension defined by the first principal component.

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$\frac{5}{7}$