Let v denote the vector space consisting of all n x n matrices with entries in f (you may assume, without givingaproof, thatv isavectorspaceoverf). let w ={aev : at =-a}, where at denotesthe transpose of the matrix a.
(a) prove that w is a subspace of v .
(b) find a finite set of elements of w that span w.
(c) find a basis for w.
(d) find dim(w).

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .