# M2700_Ch3_S1_WorkAlong.pdf - Math 2700 Notes Chapter 3,...

• 2

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 1 - 2 out of 2 pages.

Math 2700 NotesChapter 3, Section 1: Introduction to DeterminantsDefinitions:For each nxn matrix A, Aijis obtained from A by deleting row I and column j from A.The matrix A is denoted by [aij].The (i, j) cofactor of A is the Cij= (-1)i+jdet AijTheorems:If A is an nxn matrix then det A can be computed by a cofactor expansion across any row or down anycolumn.The cofactor expansion across the ith row is det A = ai1Ci1+ ai2Ci2+…+ ainCin.The cofactor expansion across the jth column is det A = a1jC1j+ a2jC2j+…+ anjCnjIf A is an nxn triangular matrix then det A is the product of entries on the main (downward) diagonal of A.If A is a 2x2 matrix then det A = the product of entries on the downward diagonal - theproduct of entrieson the upward diagonal.det A = 0 if and only if A is not invertible if and only if columns/rows of A are linearly dependent.Important Hints:When compute det A by cofactor expansion, choose the row or column with the greatest number ofzeroes to obtain the least number of computations.

Course Hero member to access this document

End of preview. Want to read all 2 pages?