Matrices/2/U to T/Describe with system of equations/1/Exercise

Let

${}U=\langle {\begin{pmatrix}4\\-7\end{pmatrix}}\rangle \subseteq K^{2}\,$

and

${}T=\langle {\begin{pmatrix}-2\\5\end{pmatrix}}\rangle \subseteq K^{2}\,.$

a) Describe the linear subspace ${}W$ of the space of all ${}2\times 2$-matrices that map the linear subspace ${}U$ to the linear subspace ${}T$, as the solution space of a linear system.

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

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

Create a solution