Question

1. compute the following linear combinations. (3 points)

a. (4(-2, 3) - 2(6, -7))
b. ((79.4, 58.1) + 3(-0.8, 6.3))

Explanation:

Step1: Scalar multiply each vector

For part a:
$4(-2, 3) = (4\times-2, 4\times3) = (-8, 12)$
$2(6, -7) = (2\times6, 2\times-7) = (12, -14)$

For part b:
$3(-0.8, 6.3) = (3\times-0.8, 3\times6.3) = (-2.4, 18.9)$

Step2: Perform vector subtraction/addition

For part a:
$(-8, 12) - (12, -14) = (-8-12, 12-(-14)) = (-20, 26)$

For part b:
$(79.4, 58.1) + (-2.4, 18.9) = (79.4-2.4, 58.1+18.9) = (77, 77)$

Answer:

a. $(-20, 26)$
b. $(77, 77)$