Matrices/3/U to T/Describe with system of equations/1/Exercise

Let

${}U=\langle {\begin{pmatrix}3\\4\\8\end{pmatrix}},\,{\begin{pmatrix}2\\1\\-1\end{pmatrix}}\rangle \subseteq K^{3}\,$

and

${}T=\langle {\begin{pmatrix}7\\1\\3\end{pmatrix}},\,{\begin{pmatrix}5\\4\\2\end{pmatrix}}\rangle \subseteq K^{3}\,.$

a) Describe the linear subspace ${}W$ of the space of all ${}3\times 3$-matrices that map the linear subspace ${}U$ into the linear subspace ${}T$, as a solution space of a linear system.

b) Describe ${}W$ by an eliminated linear system.

c) Determine the dimension of ${}W$.

Create a solution