Question

Let

u = (1, 2, 3),

v = (2, 2, −1),

and

w = (4, 0, −4).

Find 4u + 3v − w.

Answer 1

The sum of 4u, 3v, and -w is (14, 14, 5).

Step-by-step explanation:

To find 4u + 3v - w, we need to multiply each vector by its corresponding scalar and then subtract the vectors.

4u = 4(1,2,3) = (4,8,12)

3v = 3(2,2,-1) = (6,6,-3)

-w = -(4,0,-4) = (-4,0,4)

Finally, we can add or subtract the corresponding components to get the final result:

4u + 3v - w = (4,8,12) + (6,6,-3) - (-4,0,4) = (4+6-(-4), 8+6-0, 12+(-3)-4) = (14, 14, 5)