# GAUSSIAN Elimination/ Liner systems

GAUSSIAN Elimination/ Liner systems

IN ORDER TO GET FULL CREDIT FOR EACH PROBLEM,
SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY
USING THE LANGUAGE OF MATH.
The quiz is worth 100 points. Each problem is worth 5 points.
FOR #1 AND #2, PLEASE WRITE THE AUGMENTED MATRIX FOR
THE LINEAR SYSTEM.
#1 x ? 3y ? 5 2x ? y ? 3
#2 6x ?12 ?5x ? 2y ? 4
FOR #3 THROUGH #8, PLEASE SOLVE THE SYSTEM BY GAUSSIAN
ELIMINATION
#3
0 0 0
1 0 3
? ?
? ?
? ?
#4
0 1 0
1 0 3
? ?
? ?
? ?
#5
1 0 2
1 0 1
? ?
? ? ? ? ?
#6
1 3 8
2 1 9
? ?
?? ? ? ? ?
#7
4 3 15
2 5 1
? ?
? ? ? ? ?
#8
4 2 2
2 1 1
? ? ?
? ? ? ? ?
FOR #9 AND #10, SET UP THE AUGMENTED MATRIX THAT DESCRIBES THE SITUATION, AND SOLVE FOR
THE DESIRED SOLUTION.
#9 One pan pizza and two beef burritos provide 1980 calories. Two pan pizzas and one beef burrito
provide 2670 calories. Find the caloric content of each item.
#10 A hotel has 200 rooms. Those with kitchen facilities rent for \$100 per night and those without
kitchen facilities rent for \$80 per night. On a night when the hotel was completely occupied, revenues
were \$17,000. How many of each type of room does the hotel have?
FOR #11 THROUGH #15, PLEASE GRAPH THE FOLLOWING INEQUALITIES
#11 x ? y ? 2
#12 x ? y ? 2
#13 3x ? 4y ?1
#14 y ?1
#15 3y ? 3
FOR #16 AND #17, GRAPH THE SYSTEM OF INEQUALITIES. SHOW (BY SHADING IN) THE FEASIBLE
REGION.
#16 y ?1, x ? y ? 2
#17 x ? ?1, x ?1
FOR #18 THROUGH 20, GRAPH THE SYSTEM OF INEQUALITIES. SHOW (BY
SHADING IN) THE FEASIBLE REGION. IDENTIFY THE ORDERED-PAIR
“CORNER POINTS” THAT DEFINE THE FEASIBLE REGION.
#18 y ? ?x ? 4 , y ? ?3x ? 2 , x ? 0 , y ? 0
#19 x ? y ?1, x ? ?3y ? 2 , x ? 0 , y ? 0
#20 x ? y ?1, x ? 0 , y ? 0
BONUS (10 POINTS)