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According to the attached image:
Explain why G forms a field with respect to addition and multiplication. (You may quote relevant properties of matrix addition and multiplication without proof.)
Why the arithmetic F does not form a field?

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[5] 8. Let V = {x,y} be a set with exactly two vectors, r and y. Define vector addition and scalar multiplication in V by the following rules: Vector addition: 2+r= x, y + y = 1, + y = y, and y + x = y. Scalar multiplication: cx = I, and cy = y for all c ER Prove that V is not a vector space by finding one axiom in the definition of a vector space that fails to hold. You must state the axiom clearly and show it does not hold.

Harmonic function in the ball, PDE

Could someone explain how exactly is P calculated? And why we need apply xy to both b and c?

                                               

                                          

 

Solution. According to hint we look for ʯ in the form (20.3) with P a polynomial of degree 6 - 2 = 4; since g is odd with respect to x and y (separately) so P is; since g is even with respect to z so P is; since g is symmetric with respect to y  x permutation, so P is. Thus and

 

The amount of garbage, G, produced by a city with population p is given by G=f(p). G is measured in tons per week, and p is measured in thousands of people.

 

a. The town of Tola has a population of 50,000 and produces 14 tons of garbage each week. Express this information in terms of the function f.

 

Enter your answer as an equation. Do not enter an any units (people, tons) or commas in your answer.

 

Include a multiplication sign between symbols if you need to. For example, enter a*x and not just ax.

 

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b. Explain the meaning of the statement f(7)=4.

 

 

The amount of garbage produced per week by a city with population 4,000 is 7 tons.
 

The amount of garbage produced per week by a city with population 7 is 4 tons.
 

The amount of garbage produced per week by a city with population 7,000 is 4 tons.
 

The amount of garbage produced per week by a city with population 4 is 7 tons.
 

The amount of garbage produced per week by a city with population 70,000 is 4 tons.

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