ST259 Lecture Notes - List Of Farscape Characters
Document Summary
Letaemnxn f if n l so that a au we define det a a for n22 we define deta recursively as deta iscd ay dettai. Thescalar det a is called thedeterminantof a and is alsodenotedby iai thescalar. Cdi detcanid is calledthecofactor oftheentryofa in row i columnj letting a cdidetcat denotethecofactor ofthe row i columnj ofentryofa we canexpresstheformulaforthe determinantof a as def a anc arciz 1 aincin. Thusthedeterminant of a equalsthe sum of theproductsofeachentry in row 1 of a multipliedbyits cofactorthisformulais calledcofactorexpansionalong thefirst row ofa. Thfthedeterminant of an mxn matrix is a linearfunctionofeach row whentheremaining rows areheldfixedthatis for l e r e n we have detfhfi. ie detff. atij tkdet an whenever k is a scalarand u uandeach ai are row vectors in fn. Awfaem n f has a row consistingentirelyof zeros thendet a o. Let bemmmf where n 72 if row i of b equals eh for some kcieken then.
