Linear Algebra

Given the real symmetric matrix A: 2 A = 2 8 -4 1 -4 7 (a) Apply elementary row operation Ill three times to A to get upper triangular matrix U. (Do NOT use any other row ops.) (b) Construct a unit lower triangular matrix L that will undo those row ops, so that A =LU. (c) Show that U can be written as D L , wherer D is a diagonal matrix with the wwwwwww same diagonal elements as U. (d) Find L1 = L D /2, and show that A = LiLT. (e) What is the correct mathematical term for that factorization of A? (f) Which of the five types of real symmetric matrix isA? (Do NOT attempt to find the eigenvalues.)