Chapter 4 - Vector Spaces - 4.5 Basis and Dimension - 4.5 Exercises - Page 188: 67

a) $(2 s-t, s, t, s) =s(2,1,0,1)+t(-1,0,1,0)$, hence $S=\{(2,1,0,1)),(-1,0,1,0)\}$ is a basis for $W$. b) The dimension of $W$ is $2$.

Assume the subspace $W=\{(2 s-t, s, t, s) : s \text { and } t \text { are real numbers }\}$, then a) $(2 s-t, s, t, s) =s(2,1,0,1)+t(-1,0,1,0)$, hence $S=\{(2,1,0,1)),(-1,0,1,0)\}$ is a basis for $W$. b) The dimension of $W$ is $2$.