In an online game, there are three items that you can equip to increase your defence points against magical and physical attacks. The number of each item you can equip are x, y and z respecetively. The contributions and price of cach item are shown below: ITEM Magical Defence Points Physical Detence Price per Item (Coins) Points Leather Scale (x) 40 Enchanted Ruby (y) 2 20 Phoenx Feather (2) 3 100 Tahle O1 In order to clear a boss fight, you need to increase your magical defence by 20 points and physical defence by 10 points. If the total number of coins you intend to spend is 300, show that the system of lincar equations that describes the problem is: (a) [I 3 5 20 Av = b - 4 -2 3 y 10 1 5 15 Using row operations on the augmented matrix (A|b), solve the matrix equation in Question 1(a) for the number of units of cach item. Describe the system in terms of its linear independence, consisteney and rank. (b)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Question 1
In an online game, there are three items that you can equip to increase your defence points
against magical and physical attacks. The number of each item you can equip are x, y
and z respectively. The contributions and price of cach item are shown below:
ITEM
Magical
Physical
Price per
Item (Coins)
Detence
Points
Defence
Points
Leather Scale (x)
40
Enchanted Ruby (y)
3
-2
20
Phoenix Feather (z)
3
100
Table 01
In order to clear a boss fight, you need to increase your magical defence by 20
points and physical defence by 10 points. If the total number of coins you intend
to spend is 300, show that the system of lincar equations that describes the
problem is:
(a)
1 3 5
Av = b -4 -2 3
y
2 1
Using row operations on the augmented matrix [A|b), solve the matrix equation
in Question 1(a) for the number of units of cach item. Describe the system in
terms of its lincar independence, consistency and rank.
(b)
Transcribed Image Text:Question 1 In an online game, there are three items that you can equip to increase your defence points against magical and physical attacks. The number of each item you can equip are x, y and z respectively. The contributions and price of cach item are shown below: ITEM Magical Physical Price per Item (Coins) Detence Points Defence Points Leather Scale (x) 40 Enchanted Ruby (y) 3 -2 20 Phoenix Feather (z) 3 100 Table 01 In order to clear a boss fight, you need to increase your magical defence by 20 points and physical defence by 10 points. If the total number of coins you intend to spend is 300, show that the system of lincar equations that describes the problem is: (a) 1 3 5 Av = b -4 -2 3 y 2 1 Using row operations on the augmented matrix [A|b), solve the matrix equation in Question 1(a) for the number of units of cach item. Describe the system in terms of its lincar independence, consistency and rank. (b)
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