in this exercise we explore how the early stopping of the gradient descent iterations (see example )xt+ xt (xt ) is (approximatelyequivalent to the global minimization of ( gkxk for certain values of the ridge regularization parameter (see example we illustrate the early stopping idea on the quadratic function ( ( ) ( )where rnxn is symmetric positive-definite (hessianmatrix with eigenvalues {lk }nk= early stopping (averify that for symmetric matrix rn such that is invertiblewe have at- ( at )( )- (blet qlqbe the diagonalization of as per theorem if show that the formula for xt is xt ( al) qu hencededuce that necessary condition for xt to converge is maxk lk (cshow that the minimizer of ( gkxk can be written as xu ( - )- qu (dfor fixed value of tlet the learning rate using part (band ( )show that if /( aas then xt xin other wordsxt is approximately equal to xfor small aprovided that is inversely proportional to