- #1

Hall

- 351

- 81

S contains either ##(x,x,z)## type of elements or ##(x,y,x)## type of elements.

Case 1: ## (x,x,z)= x(1,1,0)+z(0,0,1)##

Hencr, the basis for case 1 is ##A = \{(1,1,0), (0,0,1)##\}

And similarly for case 2 the basis would be ##A'= \{ (1,0,1), (0,1,0)\} ##.

But how to find the basis for ##S##? A union of A and A' would give us a set whose linear span would go beyond S and hence cannot be a basis for S. Can S have a basis? How do we find it?