pleae help me to solve this questions!! Let V be the set of all ordered pairs of

Question

pleae help me to solve this questions!!

Let V be the set of all ordered pairs of real numbers (u1,u2) with u2 > 0. Consider the following addition and scalar multiplication operations on u = (u1,u2) and v = (v1,v2): u + v = (u1 + v1 + 2, 6u2v2), ku = (ku1,ku2) Use the above operations for the following parts. Compute u + v for u = (-2,1) and v = (-2,8). If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? If u = (3,), what would be the negative of the vector u refered to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)

Explanation / Answer

a . u + v =(-2-2+2 , 6*(1)*(8)) = (-2 , 48)

b. let the zero vector be O

v + O = O +v = V

let O = (x ,y )

v + O = ( -2 +x +2 , 6* 8* y) = v

x = -2

y= 1/6

O = (-2 , 1/6 )

c. null vector for u = O .

O = ( -2 ,1/6 )

u + (- u) = O

let (-U) = (x , y)

(-2+x+2 , 6*1*y ) =(-2 ,1/6)

x= -2

y= 1/36

(-u) = (-2 ,1/36)

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