Problem 3 Given an isosceles triangle ABC with AB = AC, D is a point on AB such
that AD: DB = 3:1, E is a point on side AC, and when DE and BC
are extended, they meet at a point F, such that DE: EF = 1:3.
(a) Find the ratio AD: AE.
(b) If ABDF is also isosceles, find the ratio DE : BC.

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.