MAT223H1 Lecture 12: Lecture 12 3.1 3.2(1)
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A is invertible it and only if detato where defi ad hoc. Given a nxn to bethe chin mann ithnwandjthcolumn. hn define aij obtained by deleting the. 1(cid:1266) for n 2 the determinant ofannxn matrixa is definedby. Deta adetan andetanta3detanaadettuia. nl j cofur"cij ethn1ftheti is definedby cj hi detaj. 1 the determinant ofa is denotedby vertical bars around theentries. Thmi if a is triangular then deta is the put ofthediagonalunties. Here"s atrick forcomputer determinants of 3 matrices thesumof productsalongupwarddig. How do nw operations change thedeterminant leta benxn. Then de ta detb a if a multiple ofarowofa is added to another row resulting in matrixb. If a row ofa ismultipliedby a scalarc resulting in matrixb inmatrix b then then deta detb. If then deta is an echelon form ofa. Since we cannot multiply a row by zero the constant c is nonzero. It follows that detao if and only if de two. What could the echelon form u look like.
