## Linear Algebra: A Modern Introduction

$$[6,9,-1]$$
Compute the resultant vector $x = 3b - 2c + d$ by computing each of its components. Note that $x_n = 3b_n - 2c_n + d_n$, so for each component we have: $$x_1 = 3b_1 - 2c_1 + d_1 = 3(3) - 2(1)-1=6$$ $$x_2 = 3b_2 - 2c_2 + d_2 = 3(2) -2(-2)-1=9$$ $$x_3 = 3b_3 - 2c_3 + d_3 = 3(1) -2(1)-2=-1$$ Thus, $x = [x_1, x_2, x_3] = [6, 9, -1]$