MATH Final

Question 1

If possible determine just be looking the number of points of intersection of each of the following systems and give a brief geometric reason for your answer

Answer 1

Lines: ex. 2x +3y = 5
-If y coefficient doesn’t work; one point of intersection; the lines have different slopes
-If constant doesn’t work; zero points of intersection; the lines are parallel
-If constant DOES work’ infinitely many points of intersection; the lines are the same

Planes: ex. 2x -2y + 2z
-Attack by 1:2, 1:3, 2:3
-If multiple does not work for coefficients; planes are neither the same nor parallel, cannot tell by looking
-If multiple works for all three coefficient but not constant; Planes blank and blank are parallel; zero pts. of intersection
-If multiple works for all coefficients and constant; Planes blank and blank are the same and the other is not parallel; infinitely may points of intersection
-Note: parallel planes supersedes all

Question 2

Basic and full simplex algorithm

Answer 2

basic: must be in terms of < or = to
select most (-) # in test region and pivot entry must be above horizontal bar and (+)
-if multiple positives use least c/p ratio
-if two same negative entries: choose leftmost
-if no positive entries, LPP has no solution
-two with the same least ratio; choose topmost

full: pivot entry row: most negative entry in special test region
-two same most negative entries choose leftmost
-if no negative entries in that row and to the left of the bar, LPP has no solutions

Question 3

Inverse matrix getting constant on right side of equal sign

Answer 3

take number in given constant times blank equal number from matrix