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I was thinking about using C++ to model it, but dont know what model to choose. Most of the people in my class dont really think much of matrices, as they are supposed to be "easy" with sure shot problems in exams. However, I want to illustrate that matrices are really a group of vectors and a square matrix of order n is actually n vectors bunched together in n dimensional space. Moreover, that the operations we perform on matrices are actually transformations of our original vectors. From what I understand, the n degree square matrix holds n vectors which define something analogous to a plane but in n dimensions.

Im pretty decent in C++ and my professor would be helping me along, but I dont even know where to begin looking. If someone could point out what specific "area" of mathematics/matrices I should look out, or point out specific problems, I would be really grateful. Its got to be a tough problem, something that would be challenging. Im kinda worked up about this.