Answer
The dimension of the subspace is 2
Work Step by Step
Given subspace:
$\begin{bmatrix}2\\-5\end{bmatrix},\begin{bmatrix}-4\\10\end{bmatrix},\begin{bmatrix}-3\\6\end{bmatrix}$
Let's represent the vectors as $a,b,c$ such that;
$a=\begin{bmatrix}2\\-5\end{bmatrix},b=\begin{bmatrix}-4\\10\end{bmatrix},c=\begin{bmatrix}-3\\6\end{bmatrix}$
From the set, it can be seen that $\mathbf{a}$ is a multiple of $b$.
such that;
$\mathbf{a}=\frac{b}{2}$
Hence the spanning set is reduced to $a,c$.
Since the two vectors are linearly independent the dimension of the subspace is 2
