In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.