Determinants Li Zhang Department of Mathematics Tongji University 4907 Tongji University】 1/32
. . Determinants Li Zhang Department of Mathematics Tongji University (Tongji University) Linear Algebra 1 / 32
Introduction 1.Linear Equation: a1x1+·…+amxn=b. 2.a simple systems of linear equations: a1十12x十-十41nw=b 2x1+x2+十y=b dm1十d2十十du=bn Tongji University】 2/32
Introduction 1. Linear Equation: a1x1 + · · · + anxn = b. 2. a simple systems of linear equations： a11x1 + a12x2 + · · · + a1nxn = b1 a21x1 + a22x2 + · · · + a2nxn = b2 . . . . . . am1x1 + am2x2 + · · · + amnxn = bm (Tongji University) Linear Algebra 2 / 32
Introduction 1.Linear Equation: a1x1+·…+amxn=b. 2.a simple systems of linear equations: a11x1+a12x2+··+a41mxm=b1 a21x1+a22x2+··+a2n-xn=b2 am1x1+am2X2十··+AmnXn=bm Tongji University】 2/32
Introduction 1. Linear Equation: a1x1 + · · · + anxn = b. 2. a simple systems of linear equations： a11x1 + a12x2 + · · · + a1nxn = b1 a21x1 + a22x2 + · · · + a2nxn = b2 . . . . . . am1x1 + am2x2 + · · · + amnxn = bm (Tongji University) Linear Algebra 2 / 32
Introduction 1.Linear Equation: a1x1+·…+amxn=b. 2.a simple systems of linear equations: a11x1+a12x2+··+a41mxm=b1 a21x1+a22x2+··+a2n-xn=b2 am1x1+am2X2十··+AmnXn=bm Tongji University】 2/32
Introduction 1. Linear Equation: a1x1 + · · · + anxn = b. 2. a simple systems of linear equations： a11x1 + a12x2 + · · · + a1nxn = b1 a21x1 + a22x2 + · · · + a2nxn = b2 . . . . . . am1x1 + am2x2 + · · · + amnxn = bm (Tongji University) Linear Algebra 2 / 32
Matrix Definition 7.1.1 a11... 41n .. am1 ..。amn Note:m x n matrix,square matrix,entry,order,main diagonal,row matrix, column matrix (Tongji University) 3/32
Matrix . Definition 7.1.1 . . a11 . . . a1n . . . . . . am1 . . . amn Note: m × n matrix, square matrix, entry, order, main diagonal, row matrix, column matrix (Tongji University) Linear Algebra 3 / 32