Many problems in scientific computing can be formalized as solving a large system of sparse linear equations. Iterative methods are usually employed for solving the problem, but many coefficient matrices exist where a given iterative method does not converge within a realistic time frame. When an iterative method fails, one must try another, and the time used for the first method is wasted. Suppose a method exists to predict whether a given iterative method will likely converge for a given matrix. In that case, one can save much time without running the iterative method. We trained a deep learning model (EfficientNetV2-S) to enable such classification after transforming matrices into grayscale images by scaling their components into a limited range. The proposed method achieved high predictive performance in discriminating whether the iterative method converges on a matrix. Furthermore, we found a considerable performance improvement when we introduced the pretrained neural network using a large-scale dataset of natural images (ImageNet).