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Determinants, part II Math 130 Linear Algebra D Joyce, Fall 2015 So far we've only de ned determinants of 2 2 and 3 3 matrices. The 2 2 determinants
 §B.3.1 Matrix by Vector Product .. B-7 §B.3.2 determinants and computing eigenvalues, are only de?ned for square matrices. Example B.2. C = 1263
 A Vandermonde matrix is a square matrix of the form in the theorem. Thus, in this permutation-wise sum for a Vandermonde determinant, each summand has total
 Evaluate the determinant of each matrix. 1) 0 ?4 ?6 ?2 ?24 2) ?6 0 6 ?6 36 3) ?1 1 ?1 4 ?3 4) 0 4 6 5 ?24 5) 0 ?1 6 ?6 6 6) 5 3 6 6 12
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 4.1 Overview To every square matrix A = [a ij] of order n, we can associate a number (real or complex) called determinant of the matrix A, written as det A, where a
 Notes on Matrices 4-1-2 Definition of a Matrix Matrices 4 Determinants Determinant of a 2x2 matrix: Find the determinant of each: 1. !5 ! 7 11 8 2. 3 2!1 5 3.
 Chapter 4 Determinants Chapter 3 entailed a discussion of linear transformations and how to identify them with matrices. When we study a particular linear 
 Finding the Determinant of a 4x4 Matrix . This is a recursive process. We work our way down from the 4x4 determinant to 3x3 determinants to 2x2 determinants.
 Matrices Gaussian elimination Determinants De nitions Addition and subtraction Multiplication Transpose and inverse Special cases Asquare matrix(for which m = n) is 
 Extra Practice - Determinants & Inverses of Matrices Evaluate each determinant. 1) 
 Extra Practice - Determinants & Inverses of Matrices Evaluate each determinant. 1) 
 Determinant formulas and cofactors Now that we know the properties of the determinant, This contributes 1 to the determinant of the matrix; 
 Preview The Determinant of a SQUARE Matrix More Probelms Determinant of a Matrix Satya Mandal, KU Satya Mandal, KU Determinant of a Matrix
 We now give the promised recursive de?nition of the determinant of a matrix. Since we know how to compute the determinants of 1 ?1 and 2 ?2 matrices, we start with

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