MAT 1302 Lecture Notes - Lecture 5: Augmented Matrix, Matrix Equivalence, Solution Set
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1 review linear systems and vector equa- tions. Last class we went through some introductory de nitions that will start us on the way to studying vector spaces. In particular, we saw the de nition of vectors as column matrices and of the operations of addition and scalar multiplication on them. The class ended by showing that it is possible to state questions about solutions to linear systems in this new language. Every linear system is equivalent to a vector equation. 1 is also a solution of the linear system. Any solution to this equation (which recall, means that combination of. Conversely, any solution to this linear system is a solution to the vector equation. They are two di erent ways of writing down the same problem. One can actually be obtained from the other by using the rules of vector addition and scalar multiplication we learned last class: