In this chapter we present examples from one of the most important applications of linear algebra, to systems of differential equations. We have seen how the use of matrices makes it possible for us to handle systems of k equations in n unknowns, and to interpret these as representing linear transformations between spaces. We now see how the use of linear algebra makes it possible to approach systems of equations involving derivatives of functions. For this chapter, a knowledge of calculus of one variable is assumed.
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