ST259 Lecture : 4.3 - Properties of Determinants
Document Summary
If e is an elementarymatrixobtainedbyinterchanginganytworows of i thendet e. Ife is an elementar matrixobtainedby multiplying some row of i bythe nonzero scalar k thendeffe k. Ife is an elementar matrix obtained byadding amultipleof some row of i to another row detceei. Tha4. 7foranya bemmm f def ab detca det b. Va matrix acmmm f isinvertible iff det a to furthermore if a isinvertible then delcad 1 detca. Let ax b bethematrixform of asystem of n linearequations in n unknowns xn t if deta to thenthissystem has a unique solution andforeach k. He detox delca where mk is themxn matrix obtainedfrom a byreplacingcolumn k ofabyb an respectivelythen idetcahisthenthdimensionalvolumeofthe. If therows of a are a az parallelepiped havingthevectors a az.
