Hi I am now filling in what I perceive to be gaps in my knowledge. One of these problems is understanding why matrices can solve systems of equations. I do completely get Gaussian elimination to solve systems of linear equations. However, when using determinants and the like to solve, for instance, systems of differential equations, I do not feel I have properly learned why that works. Whenever I pick up a book on systems theory, I am reminded that I understand metric spaces and Lebesgue integration better than something as basic as a matrix. I need to change that. What book can, through a rigorous manner, explain matrix theory to me?