Applying the rules of addition and scalar multiplication of vectors, –4w = (–8, 20) and –4u + w = (6, –7)
In the 2D coordinate system, vectors can be split into x-component and y-component.
we can write, for example, a vector r = (2,–6), which means:
x-component = 2
y-component = –6
- Addition / subtraction of vectors: Just add or subtract the corresponding components.
For example: r = (2,–6) and s = (-2,3)
Then,
r + s = (2,–6) + (-2,3) = (2–2, –6+3) = (0,–3) - Scalar multiplication: Multiply each component by the given scalar.
For example: r = (2,–6)
Then,
6r = 6.(2,–6) = (6 . 2, 6 . (–6)) = (12,–36)
In the given problem:
u = (-1,3), v = ( 2,4) , and w = (2,-5)
Then,
–4w = –4(2, –5)
= (–4 . 2, –4. (–5)) = (–8, 20)
–4u + w = –4(-1,3) + (2, –5)
= (–4.(–1), –4 . 3) +(2, –5)
=(4, –12) + (2, –5)
= (4+2, –12–(–5)) = (6, –7)
Learn more about vector addition and scalar multiplication here:
brainly.com/question/13592198
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