5.1.3 Affine transformations

Problem: Affine span of a set \( \left\{(1,1,1,1),\left(1, \frac{3}{2}, 1, \frac{3}{2}\right),(2,1,2,1)\right\} \) parallel to the line passing through the points \( (1,0,0,0) \) and \( (3, a, 2,1) \), for \( a=\cdots \).