A neural network unit computes a non$-$linear weighted combination of its input:

where are numbers called weights $,$ is a number and is the weighted sum of the inputs and is generally a non$-$linear function called the activation function $.$

The above equation in vector form is:

where and $.$

Numerical Example $-$ Neural Network Unit

$2$ points possible $($graded$)$

In this problem, you will compute the output in the following neural network unit with $2$ inputs and $.$