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)
Please solve
2 5 1 5
1 4 2 1
4 10 1 1
? ?
? ?
? ?
?? ? ??
by Gaussian Elimination.

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