Homework SourseExpress the vector v 24 38 as a linear combination of x 2
Express the vector v = [24 -38] as a linear combination of x = [-2 3] and y = [3 -5]. The vectors v = [1 2 2], u =[-1 1 4 + k], and w = [-3 5 16]. are linearly independent if and only if k notequalto.![Express the vector v = [24 -38] as a linear combination of x = [-2 3] and y = [3 -5]. The vectors v = [1 2 2], u =[-1 1 4 + k], and w = [-3 5 16]. are linearly](/WebImages/24/express-the-vector-v-24-38-as-a-linear-combination-of-x-2-1061624-1761554682-0.webp "Express the vector v = [24 -38] as a linear combination of x = [-2 3] and y = [3 -5]. The vectors v = [1 2 2], u =[-1 1 4 + k], and w = [-3 5 16]. are linearly")
Solution
linear representation of given vectors:
-2x + 3y = 24 and 3x - 5y = -38
solve this system, we get
x = -6 and y = 4
then
v = -6x + 4y
