Find the vector w=2u-3v and its additive inverse.

Question

Let u=(1,-1,0) and v=(1,-2,-3).
Find the vector w=2u-3v and its additive inverse.

w=

-w=

 

Answer 1

If u = (1, -1, 0), then 2u = 2*(1, -1, 0) = (2, -2, 0)

If v = (1, -2, -3), then 3v = 3*(1, -2, -3) = (3, -6, -9)

 

w = 2u - 3v = (2, -2, 0) + (3, -6, -9)

= (2+3, -2+-6, 0+-9)

= (6, -8, -9)

 

To find -w,  you multiple each component of w by -1:

-w = -1*(6, -8, -9) = (-6, 8, 9)

 

Hope this helps!

 

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