## Question

###### 2.1 Deviation of middle element value from average. Suppose 1 21. We dlefine the middlle element Value of' a5 Tmn * Definen-vectol, with2m - 1 andf() = CmTi; i=lwhich is the difference hetween the midldle element value and the average of the coefficients in Express f in the form f() =(lI. where a is a n-vector 2.2 Nonlinear functions. Show that the following two functions f R3 4 R are not linearf(z) = (x1 T2 + 13)2 f(z) (81 + 272 13 + where for any real number &, (a) - is the positive p

2.1 Deviation of middle element value from average. Suppose 1 21. We dlefine the middlle element Value of' a5 Tmn * Define n-vectol, with 2m - 1 and f() = Cm Ti; i=l which is the difference hetween the midldle element value and the average of the coefficients in Express f in the form f() =(lI. where a is a n-vector 2.2 Nonlinear functions. Show that the following two functions f R3 4 R are not linear f(z) = (x1 T2 + 13)2 f(z) (81 + 272 13 + where for any real number &, (a) - is the positive part of &, defined as (a)+ max{a, 0}. Remark:. This function is widely used in neural networks, where is it called the relu function. shortening of rectified linear unit.

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