Given g = (3, -5) and h = (-4, 6), find 4g + 3h.
To find 4g + 3h, we need to multiply each component of g and h by their respective scalars and then add the results.
Multiplying g by 4, we get:
4g = 4 * (3, -5) = (4*3, 4*(-5)) = (12, -20)
Multiplying h by 3, we get:
3h = 3 * (-4, 6) = (3*(-4), 3*6) = (-12, 18)
Now, we add the results:
4g + 3h = (12, -20) + (-12, 18) = (12+(-12), -20+18) = (0, -2)
Therefore, 4g + 3h = (0, -2).