Exam 2025 (A)

4a

\begin{matrix} Let V \\ Let U, W \subseteq V : U \cap W = {0} \\ Then \exists T : V \to V : k e r T = U, I m T = W \\ U = s p {(\begin{matrix} 1 \\ 0 \\ 0 \end{matrix})}, W = s p {(\begin{matrix} 0 \\ 1 \\ 0 \end{matrix})} \\ U \cap W = {0} \\ T (\begin{matrix} x \\ y \\ z \end{matrix}) = (\begin{matrix} . \\ . \\ . \end{matrix}) \\ k e r T = U \\ I m T = W \end{matrix}