Chapter 4 - Vector Spaces - 4.1 Vectors in Rn - 4.1 Exercises - Page 153: 33

$$w=(\frac{1}{2},-\frac{7}{2},-\frac{9}{2},2)$$

Let $u=(1,-1,0,,1)$, $v=(0,2,3,-1)$, we have $$w=\frac{1}{2}(u-3v)=\frac{1}{2}((1,-1,0,1)-3(0,2,3,-1))\\ =\frac{1}{2}((1,-1,0,1)-(0,6,9,-3))\\ =\frac{1}{2}(1,-7,-9,4)=(\frac{1}{2},-\frac{7}{2},-\frac{9}{2},2)$$