 Solution

If $g=\nabla f(x)\ne 0$, the positive-definite symmetric matrix $B$ is an invertible matrix and $s=-B^{-1}g\ne 0$. Multiplying $Bs=-g$ by $s^T$ givesHence $s$ is a descent direction. If $g=0$, then $s=0$ and the algorithm has already reached a stationary point; the strict descent assertion applies before termination.