Given vectors u = (4, -1) and v = (2, 3), what is the vector 3u - 2v?
Show the answer and explanation
Correct answer
A. (8, -9)
Principle or equation
Vector scalar multiplication and subtraction are performed component-wise: k(u1, u2) = (ku1, ku2) and (a, b) - (c, d) = (a - c, b - d).
Why this answer is correct
3u = 3(4, -1) = (12, -3). 2v = 2(2, 3) = (4, 6). Then 3u - 2v = (12 - 4, -3 - 6) = (8, -9).
Example
If a = (1, 2) and b = (3, 4), then 2a - b = (2, 4) - (3, 4) = (-1, 0).
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