need help with question 4

Question 3 Consider the following symmetric matrix over the field of real numbers, (a) (6 Marks] Find eigenvalues, eigenvectors and basis of the eigenspaces of A. (b) [& Marks] Find an orthonormal basis for each of the eigenspaces of A. () [# Marks] Using part (b), determine, if possible, an orthogonal matrix Q such that A - QDQ , where D is a diagonal matrix. Question d Consider the following bilinear from on R3 where a = (21, Ja, as )' and y - (th, 92. va) are vectors in R3. (a) [5 Marks] Find the matrix representation of B(r, y) with respect to the standard basis (eres, es} of R. (b) [4 Marks] Looking at part (e) of Question 3, find a basis y of R' such that B(r, y) is represented by a diagonal matrix with respect to y. (c) [1 Mark] Find the quadratic from K(2) : R' - R, such that K(x) = B(x, r) = Jagr.x;, ij=1 where 3, Ja, d's are the coordinates of a E R' with respect to the ordered basis {e1, e2, e3} (d) [2 Marks] Let S denote the surface in R3 determined by the equation K(r) = 0 with respect to the standard basis {c1, ca, ca}, where K(a) is as defined in part (c). Using the