The aim of this question will be to produce matrices with specified eigenvalues which are not just triangular! Let p(x) be the polynomial p(x) = x" + an_1x"-+ ...+ aix+ do, and define the companion matrix to the polynomial as -an-1 - an-2 . . . -a1 -ao O . . . C(p) = . . . O ... . O - O . .. (1) Write down the matrix C(p) of the polynomial p(x) = x3 - 4x2 + 5x - 2 (2) Find the characteristic polynomial of the matrix C(p) which you wrote in the previous step. (3) Show that + N - is an eigenvector of C(p) with eigenvalue 2. (3) Find the matrix C(p) associated to the polynomial p(x) = x3 + ax2 + bx + c (4) Determine the characteristic polynomial of the matrix C(p) from the previous step (5) Show that if A is an eigenvalue of the companion matrix C(p), then is an eigenvector of C(p) corresponding to 1 (6) Construct a non-triangular 3 x 3 matrix with eigenvalues -2, 1, 3 using companion matrices. Briefly justify your answer. Note: There was a discrepancy between the eigenvalues given on Assign 2 (they were 5, 3, 1) and on the PDF on eClass. I've corrected this-- but if you solved the problem for 5, 3, 1 this is also fine. Just write clearly which three eigenvalues you used