Vectors: Solve the following equations for the vector x ∈ ℝ2

Question

x ∈ ℝ²

(a) −2x + (0, −1) = (−2, 1)

(b) (−4, 0) − x = (1, −1) − 2x

(c) 2(x + 2(x + 2x)) = 5(x + 5(x + 5x)

Answer 1

a) -2x + [0,-1] = [-2,1] could be written as -2x = [-2,1] - [0,-1] = [-2,2]. Dividing by -2 on both sides, we get

x = [1,-1]

b) (−4, 0) − x = (1, −1) − 2x could be written as (−4, 0) - (1, −1) =− 2x + x = -x which is (−4, 0) - (1, −1) = -x

or multiplying by -1 we get x = (1, −1)-(−4, 0)=(5,-1)

c)2(x + 2(x + 2x)) = 5(x + 5(x + 5x) is 2(x + 2x + 4x) = 5(x + 5x + 25x) or 2(7x) = 5(31x) or 14x = 155x which means that (14-155)x = 0 so we get that x = 0