Modify the LDL' Factorization Algorithm as suggested in the text so that it can be used to solve linear systems. Use the modified algorithm to solve the following linear systems. a. 2x\ X2 =3, -x\ + 2x2 - Xi - -3. - X2 + 2x3 = 1 c. 4x| + X2 - X3 =7, X, + 3X2 -*3 =8, X| X2 + 5X3 + 2X4 = 4, 2x3 + 4x4 = 6. b. 4xi + X2 + X3 + X4 = 0.65, X| + 3x2 X3 + X4 = 0.05, X| X2 + 2X3 =0. X| + X2 -f- 2x4 0.5. d. 6x1 + 2x2 + *3 X4 = 0, 2xi + 4x2 "P -^3 7, + X2 + 4X3 - X4 = -1, X] X3 + 3x4 = 2.

2/5/18 Lecture Monday, February 512:05 PM Challenge: x + y 42 x 2 + 4x 6y 8z = 13, is what surface Draw it! Quadric Surfaces Def. 2 3 What surface is described by z = y in R 3 Def. A cylinder S is a surface in R is made of all lines, called the ruling of S, that are parallel to a given line l, and pass through points on a given plane C. So our curve z = y is a parabolic cylinder. (normally taught cylinders are circular cylinders) 3 Quadratic surfaces in R 2 Quadratic surfaces in R Ax + by 3 Classification of quadric surfaces in R if one variable is missing cylinders (the third va