MAT223H1 Chapter Notes - Chapter 5.2: Laplace Expansion, Determinant
Document Summary
We focus on properties of determinants that could make its computation faster than the cofactor expansion method. We will use row operations to make computing determi- nants more ef cient. The rst method we will explore consists in taking a ma- trix to its echelon form and then computing the determi- nant as the multiplication of its diagonal elements. Theorem 1 summarizes the effects of using row operations on determinants. If a and b are both n n matrices, then det ab = det a det b. Let a and b be n n matrices. Let a be an n n invertible matrix. Let p be a partitioned n n matrix of the form (cid:21) (cid:20) a b. C d or p = where a and d are square block summaries. 1 c det b. (1b) (c) suppose that b is produced by adding a multiple of one row of a to another.
