2. (10 points) in Lecture 2-2, we gave the normal equation (i.e., closed-form solution) for linear regression using MSE as the cost function. Prove that the closed-form solution for Ridge Regression is w = (a1 + XT.x)-1. T. y, where I is the identity matrix, X = (x(1), x(2),...,x(m))" is the input data matrix, x0 = (1, X1, X2,...,xn) is the ith data sample, and y = (y(1),y(2),...,y). Assume the hypothesis function hw (x) = Wo + Wix, + W2X2 + ... + WnXn, and y) is the measurement of hw(x) for the j th training sample. The cost function of the Ridge Regression is E(w) = 2.(wx - y) + A2, w. Normal Equation (closed-form solution): W = (X. x)-1.xt.y W: the value of that minimizes the cost function X: the training data set y: the vector of target values containing y(1) to y(m) 2. (10 points) in Lecture 2-2, we gave the normal equation (i.e., closed-form solution) for linear regression using MSE as the cost function. Prove that the closed-form solution for Ridge Regression is w = (a1 + XT.x)-1. T. y, where I is the identity matrix, X = (x(1), x(2),...,x(m))" is the input data matrix, x0 = (1, X1, X2,...,xn) is the ith data sample, and y = (y(1),y(2),...,y). Assume the hypothesis function hw (x) = Wo + Wix, + W2X2 + ... + WnXn, and y) is the measurement of hw(x) for the j th training sample. The cost function of the Ridge Regression is E(w) = 2.(wx - y) + A2, w. Normal Equation (closed-form solution): W = (X. x)-1.xt.y W: the value of that minimizes the cost function X: the training data set y: the vector of target values containing y(1) to y(m)