Data vectors $x=(x_1,$dots,$x_4)$ are augmented to give expanded features

$(x)=(x_1,$dots,$x_4,x_1^2,$dots,$x_4^2,x_1{x}_2,$dots,$x_3{x}_4).$

$($a$)$ What is the dimension of $(x)?$

$($b$)$ The Perceptron algorithm is run using the basis expansion $(x)$ and returns $w,b.$ What is the

dimension of $w?$