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

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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.

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Term
Fall
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Tags
Determinant, Characteristic polynomial, Det, matrix A, nxn matrix A

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