Compute the space and time complexities $($in the form of big $O,$ consider only the training stage$)$ of the following algorithms:

$[6$ points$]$

$3$

$($a$)$ Ridge regression $($Question $2($b$))$ with the closed$-$form solution

$($b$)$ PCA $(N$ data points of $D-$dimension, choose $d$ principal components$)$

$($c$)$ Neural network with architecture $D-H_1-H_2-K$ on a mini$-$batch of size $B($consider only the forward process and neglect the computational costs of activation functions$)$

$[$Hint: the time complexity of $Ain{R}^{mn}Bin{R}^{nl}$ is $O(mnl)$; the time complexities of eigenvalue decomposition and inverse of an $nn$ matrix are both $O(n^3).]$