(b) Consider a more general case (not specific to the aforementioned samples): PCA performs linear dimensionality reduction with zt w Txt, where x e IRD is the original data for the t-th sample, zt e Rd is the low-dimensional projection (d < D), W e IRID xd is the PCA projection matrix (each column is a principal component). Professor HighLowHigh claims that we can reconstruct the original data with v t Wzt, so that Vt v t Xt. Is the claim correct? Explain your answer with necessary details (you can use formulations if it helps explain)