Orthogonal complement of the subspace spanned by $$$\left[\begin{array}{c}7\\24\end{array}\right]$$$, $$$\left[\begin{array}{c}0\\1\end{array}\right]$$$

Find the orthogonal complement of the subspace spanned by $$$\mathbf{\vec{v_{1}}} = \left[\begin{array}{c}7\\24\end{array}\right]$$$, $$$\mathbf{\vec{v_{2}}} = \left[\begin{array}{c}0\\1\end{array}\right]$$$.

Since every vector in the orthogonal complement should be orthogonal to every vector in the given subspace, we need to find the null space of $$$\left[\begin{array}{cc}7 & 24\\0 & 1\end{array}\right]$$$.

The basis for the null space is empty (for steps, see null space calculator).

Thus, the orthogonal complement has no basis.

The orthogonal complement has no basis.