Chapter 4 - Vector Spaces - 4.1 Vectors in Rn - 4.1 Exercises - Page 153: 31

(a) $u+2v= (1,6,-5,-3)$ (b)$w-3u=(-1,-8,10,0)$ (c) $4v+\frac{1}{2}u-w= (-\frac{3}{2},11,-\frac{13}{2},-\frac{21}{2})$

Let $u=(1,2,-3,1)$, $v=(0,2,-1,-2)$, $w=(2,-2,1,3)$ (a) $u+2v=(1,2,-3,1)+2(0,2,-1,-2)=(1,6,-5,-3)$ (b)$w-3u=(2,-2,1,3)-3(1,2,-3,1)=(-1,-8,10,0)$ (c) $4v+\frac{1}{2}u-w=4(0,2,-1,-2)+\frac{1}{2}(1,2,-3,1)-(2,-2,1,3)=(-\frac{3}{2},11,-\frac{13}{2},-\frac{21}{2})$