Question

Find the ordered triple to represent u in u=3v-2/3w +2z if v=(4,-3,5) w=(2,6,-1) and z=(3,0,4)

Answer 1

u=(14/3 ,-13,23/3)

Explanation:

Given

u=3v-2/3 w+2z

And

v=(4,-3,5)

w=(2,6,-1)

z=(3,0,4)

Putting the values of v,w and z

u=3(4,-3,5)-2/3 (2,6,-1)+2(3,0,4)

u=(12,-9,15)-(4/3,12/3,-2/3)+(6,0,8)

=(12,-9,15)-(4/3,4,-2/3)+(6,0,8)

We will perform the addition first..

=(12,-9,15)-(4/3+6 ,4+0,-2/3+8)

= (12,-9,15)-(22/3,4,22/3)

Subtraction will give us:

=(12-22/3 ,-9-4 ,15-22/3)

=(14/3 ,-13,23/3)