solution of linear equations by elementary rows operation Teaching Request】 1. Understanding n-dimension vector; linear combination and linear represented of vectors 2. Understanding the definition of linear dependent and independent of vector collection; Knowing the properties and the way to determine the vector collection are linear dependence or nce 3. Mastering the maximal linearly independent collection of vector and rank of vectors Solve maximal linearly independent collection of vector and the rank of vectors 4. Knowing the conception of vector collections equal Understanding the relations between vector collection's rank and matrixs rank 5. Knowing the conception of n-dimension vector; subspace; basis; dimension 6. Understanding the basis for solutions of system, solutions and solution vector of omogeneous linear equations 7. Understanding the structure of solution and solutions of non-homogeneous linear quations 8. Mastering the way to solve the solution of linear equations by elementary row operation (The Key Points I Linear dependence and independence of vectors; The maximal linearly independent collection and the rank of vectors The way to solve the solution of linear equations by elementary row s operation the Difficulty Points] The conception of vector space; Linear dependence and independence of rectors; Solution space and the basis for solutions of system Depth and breadth I Understanding n-dimension vector; Mastering linear dependence and independence of vectors; Can solve maximal linearly independent collection of vector and he rank of vectors Chapter 5 Eigenvalues Eigenvectors and Quadratic Forms Teaching content】 Eigenvales and eigenvectors of matrix; Inner product; Form linear independence to orthogonal by Gran-Schmidt method; Orthogonal basis; Similar transformation and similar matrix's conception and properties; Full essential condition of diagonalizable and triangular matrix; Quadratic Forms and its matrix form; Rank of Quadratic Forms; Diagonal quadratic fom; Positive definite quadratic forms and positive definite matrices. Teaching Request】 1. Understanding eigenvales and eigenvectors of matrix Can solve eigenvales and eigenvectors 2. Form linear independence to orthogonal by Gram-Schmidt method 3. Understanding similar matrix and knowing full essential condition of diagonalizable 4. Knowing Quadratic Forms and its rank; orthogonal and Positive definite theorem 5. Mastering Quadratic Forms matrix, the way form diagonalizable by orthogonal transformation 6. Knowing quadratic Forms and its matrix's positive definite, Determine of positive definite (The Key Points l Similar matrix; Eigenvales and eigenvector's solution; Diagonalizable of real symmetric matrix; Form diagonalizable by orthogonal transformation. Quadratic Forms and its matrix's positive definite: Determine of positive definitesolution of linear equations by elementary row’s operation. 【Teaching Request】 1. Understanding n-dimension vector; linear combination and linear represented of vectors. 2. Understanding the definition of linear dependent and independent of vector collection; Knowing the properties and the way to determine the vector collection are linear dependence or independence. 3. Mastering the maximal linearly independent collection of vector and rank of vectors; Solve maximal linearly independent collection of vector and the rank of vectors. 4. Knowing the conception of vector collection’s equal ; Understanding the relations between vector collection’s rank and matrix’s rank.. 5..Knowing the conception of n-dimension vector; subspace; basis; dimension. 6. Understanding the basis for solutions of system, solutions and solution vector of homogeneous linear equations. 7. Understanding the structure of solution and solutions of non-homogeneous linear equations. 8. Mastering the way to solve the solution of linear equations by elementary row’s operation. 【The Key Points】Linear dependence and independence of vectors; The maximal linearly independent collection and the rank of vectors; The way to solve the solution of linear equations by elementary row’s operation . 【the Difficulty Points】The conception of vector space; Linear dependence and independence of vectors; Solution space and the basis for solutions of system. 【Depth and breadth】Understanding n-dimension vector; Mastering linear dependence and independence of vectors; Can solve maximal linearly independent collection of vector and the rank of vectors. Chapter 5 Eigenvalues 、Eigenvectors and Quadratic Forms 【Teaching Content】 Eigenvales and eigenvectors of matrix; Inner product; Form linear independence to orthogonal by Gran-Schmidt method; Orthogonal basis; Similar transformation and similar matrix’s conception and properties; Full essential condition of diagonalizable and triangular matrix; Quadratic Forms and its matrix form; Rank of Quadratic Forms; Diagonal quadratic form; Positive definite quadratic forms and positive definite matrices.） 【Teaching Request】 1. Understanding eigenvales and eigenvectors of matrix; Can solve eigenvales and eigenvectors of matrix;) 2．Form linear independence to orthogonal by Gram-Schmidt method. 3. Understanding similar matrix and knowing full essential condition of diagonalizable. 4. Knowing Quadratic Forms and its rank; orthogonal and Positive definite theorem. 5. Mastering Quadratic Forms matrix ,the way form diagonalizable by orthogonal transformation. 6. Knowing quadratic Forms and its matrix ‘s positive definite, Determine of positive definite. 【The Key Points】Similar matrix; Eigenvales and eigenvector’s solution; Diagonalizable of real symmetric matrix; Form diagonalizable by orthogonal transformation. Quadratic Forms and its matrix ‘s positive definite; Determine of positive definite