Question

Given u = {-4,7) and y = (5,2), compute the following:

a. u+v
b. u-v
c. -4u
d. 3u - 60
e. 2u+v-4u

Answer 1

Answer with explanation:

Given :
`u = (-4,7)\text{ and } v= (5,2)` [ Since the value of v is not mentioned , so we assumed y to be v to elaborate the procedure to solve the question)

To evaluate : a. u+v

b. u-v

c. -4u

d. 3u - 60

e. 2u+v-4u

a.
`u+v = (-4,7)+(5,2)= (-4+5, 7+2)=(1,9) \ [\because (a,b)+(c,d)=(a+c,b+d)]`

b.
`u-v = (-4,7)-(5,2)= (-4-5, 7-2)=(-9,5) [\becausek(a,b)=(ka,kb)]`

c.
`-4u= -4(-4,7)=(-4*-4,-4*7)=(16,-28)`

d.
`3u - 60= 3(-4,7)-(6,0)=(-12,21)-(6,0)=(-12-6,21-0)=(-18,21)`

e.
`2u+v-4u= 2u-4u+v=-2u+v=-2(-4,7)+(5,2)=(8,-14)+(5,2)=(13,-12)`