We assume that there are 10 samples in the training data set {(xp,yp),p=1,2,,10} where xpR21 and ypR11. We define X^R310 as the reconstructed data set matrix and y as the vector containing all the labels for the 10 samples. X^=[x^1x^2x^10]y=y1y2y10 We use Linear Regression model: y~=w^Tx^ and apply L2 loss with L2 regularization as the training objective function: minimizeE2R(w^)=101p=110(w^Tx^pyp)2+w^22 a) ( 9 points for ECE 403, 8 points for ECE 503 ) Given Eigen-decomposition of matrix X^X^T X^X^T=UUT0.70.700010.70.7020000400010.700.70.700.7010 and vector X^y X^y=112 compute the optimal model w^1,w^2,w^3 with 1=0.1,2=0.2,3=0.6, respectively. For validation data set (x1(v),y1(v))=([11],1)(x2(v),y2(v))=([33],2) compute the validation error RMSEvalidation=[21l=12(w^Tx^l(v)yl(v))2]21 with w^1,w^2,w^3, respectively. c) (1 point) Based on the final output model after validation, predict the label of one test data sample x=[55]