Which algorithm in Deep learning can verfity the relationship of column into a matrix
You can all simply use DNN, however the results are not that good compared with ML but there is no way to solve that.
I'm reading these days about deep learning and its utilization and the methods we can use it. I had a general question regarding the image verification or let's say a simple matrix. 
Suppose I have a matrix of size X = (4,4) and a vector of size Y = (1,4), I multiplied the the vector Y by only one column from X, let's say the second column. Hence, Z = Y.*X(:,2). Suppose I know the matrix X and resulted vector Z, can I use the deep learning to verify which column from X was multiplied based on Z and X ? 
I know, we can all simply use Maximum likehood decoder, or by divided X/Z ; In reality I need to avoid these conventional ways and go to deep learning. Can we do that using deep learning? which algorithm can be used in that case ?