MAT223H1 Lecture 9: Lecture 9 2.5
Document Summary
Recall to solve a wecanfinda and compute a lj. It turns out that in computing with computers finding a introduces too manyroundof errors. Defh an lu factorization of an mxn matrix a is pairof matrices ii forj. Whyisthiy suppose l and uare an lu factorizationofa. Then a canbe rewritten as l ut or . Thus we cansolve by first solving lj andthesolvingwig t get . Lmxm lower triangular with i"s onthediagonal u mxn. in echelon form and ain. Howa final and u for a givena u is found by reducing a to an echelonform. Suppose that finding theechelonform u involved no low interchanges. Then the sequence of elementary matrices epthat bring ato echelon form uli. e. lk ep eia is st each matrixei epislowertriangular. The corresponding elementary matrix is fff this is alowertriangular man. The inverse of a lower triangularmatrixwithi"s onthediagonalis also a lowertrainguarmatrixwithi"s onthediagonal.
