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1、Sec.4 Cramers Rule(克拉默法则),1.System of Linear Equations,2.Cramers Rule,3.Review and Questions,1.System of Linear Equations(线性方程组）,Linear Equation:,System of linear equations:,n unknowns,m equations,(1),When m=n,that is,n unknowns（未知量）,n equations,The Coefficient Determinant（系数行列式）of the linear system
2、.,then,If,2.Cramers Rule Theorem 1,Then the LS has a unique solution which are got as:,Proof,If(1)has solution,then,Hence we have,Example 1 Solve the linear equations using Cramers rule:,Solution.,The Coefficient Determinant of this LS is:,so,When the right-hand side members,are all zero,(1)become,W
3、hen,arent all zero,The LS is called non-homogenous system of linear equations.(非齐次线性方程组),(2),Homogenous System of Linear Equations（齐次线性方程组）,Has only zero solution,Has many nonzero solutions,In another word,We call it the trivial solution(零解),So when,the system has nontrivial solutions.,Solution:If t
4、he system has nontrivial solution,the coefficient determinant must be zero.,How to calculate?,Review,1.Under what condition can we use the Cramers rule?,2.The formula of the Cramers rule,Question:,Please find the linear equation which passes point,Solution:,Suppose the linear equation is,There must be,Where a,b,c cannot be all zero.,So we have:,Taking a,b,c as unknowns,it means(1)has nontrival solution.,So the coefficient determinant of(1)is 0,it follows that,(2)is a linear equation.,Since satisfy(2),(2)Must be the linear equation we need.,
