Question 13: Which of the following affine subspaces was considered b…

The teacher asked Soumya and Sohini to consider an affine space each. Soumya considered the affine subspace $L$ and Sohini considered the affine subspace $L'$ of $\mathbb{R}^3$, where $L = U$ and $L' = (2,0,1) + U'$, for some vector subspaces $U = Span\{(2,0,1), (1,1,0), (0,1,0)\}$ and $U' = Span\{(1,0,1), (0,1,1)\}$ of $\mathbb{R}^3$. Suppose there is a linear transformation $T : U \to U'$ such that $(0,1,0) \in ker(T)$, $T(2,0,1) = (0,1,1)$ and $T(1,1,0) = (1,0,1)$. An affine mapping $f : L \to L'$ is obtained by defining $f(u) = (2, 0, 1) + T(u)$, for all $u \in U$. By using the above information answer the given subquestions:

Which of the following affine subspaces was considered by Soumya?