Let u = (1, 3) and v = (-2, 4). Calculate (a) u + v; (b) 3u; (c) – v; (d) u – v; and (e) – 3u + 5v.
Chapter 1
Q. 1.4
Step-by-Step
Verified Solution
\begin{aligned}&\text { (a) }\mathbf{u}+\mathbf{v}=(1+(-2), 3+4)=(-1,7) \\&\text { (b) }3 \mathbf{u}=3(1,3)=(3,9) \\&\text { (c) }-\mathbf{v}=(-1)(-2,4)=(2,-4) \\&\text { (d) }\mathbf{u}-\mathbf{v}=\mathbf{u}+(-\mathbf{v})=(1+2,3-4)=(3,-1) \\&\text { (e) }-3 \mathbf{u}+5 \mathbf{v}=(-3,-9)+(-10,20)=(-13,11)\end{aligned}