18.02 Lecture Notes - Lecture 1: If And Only If
Document Summary
Lines in r as you change c you are translating the parallel lines[ There are in nitely man equations for each line given by multiplying through by scalar. The solution is the intersection of these two lines. There are no solutions if the lines are parallel, they never intersect. There are in nitely many solutions if the lines are parallel. The lines are parallel iff det| | = 0. We can write the system of the equations using matrices. If the determinate of a = 0, then the inverse of a exists. Recall a a = a a = i. We showed that if the determinant does not equal zero, there i s exactly one solution. Then a is mxm and the determinant of a does not equal zero. If the determinant of a does not equal zero, there is exactly one solution.
