Problem 1. (20 points) Given 2 A = 2 8 0 -2 0 24 1. Find the LU decomposition of A such that A = LU where L is unit lower triangular and U . is upper triangular. 2. Find the LDL" decomposition of A such that A = LDL where L is unit lower triangular and D is diagonal. 3. Use the LDL" decomposition above to find the decomposition A = L'LT, where L' is lower triangular with positive diagonal entries. 4. Show that the matrix A is symmetric positive definite. (Hint: use A = L'LT.) use A= LILIAT' and the definition of positive definitness. - b where