Goals and objectives  Course Outcomes  

1.  The students can use basic operations of matrices to solve a linear equation with Gaussian elimination. 
A1

2.  The students can raise concrete & nontrivial examples of the four fundamental vector subspaces and for each such example, you can find a basis and determine its dimension. 
A1

3.  The students can use GramSchmidt to find an orthonormal basis for a given subspace of a vector space. 
A1

4.  The students can use eigenvariables & eigenvectors of a given matrix A to diagonalize A and to compute the power of A as well as solve the linear differential equation given by A. 
A1

5.  The students can determine the corresponding linear transformation given a change of basis of a vector space. 
A1

Class schedule  HW assignments (Including preparation and review of the class.)  Amount of Time Required  

1.  The geometry of linear equations Elimination with matrices 
Review the content of the lecture (1.11.3, 2.12.3 in the textbook)  200分 
Work on homework problems  180分  
2.  Matrix operations and inverses Elimination and factorization 
Review the content of the lecture (2.42.6 in the textbook)  160分 
Work on homework problems  220分  
3.  Transposes and permutations Vector spaces and subspaces 
Review the content of the lecture (2.7, 3.1 in the textbook)  120分 
Work on homework problems  260分  
4.  The nullspace The complete solution to Ax = b 
Review the content of the lecture (3.23.3 in the textbook)  160分 
Work on homework problems  220分  
5.  Basis and dimension The four fundamental subspaces 
Review the content of the lecture (3.43.5 in the textbook)  160分 
Work on homework problems  220分  
6.  Orthogonality Projections and subspaces 
Review the content of the lecture (4.14.2 in the textbook)  120分 
Work on homework problems  240分  
7.  Midterm presentation and discussions on the solutions afterwards  Preparation for the midterm presentation  380分 
8.  Least squares approximations Orthonormal bases and GramSchmidt 
Review the content of the lecture (4.34.4 in the textbook)  140分 
Work on homework problems  240分  
9.  Properties of determinants Formulas for determinants 
Review the content of the lecture (5.15.2 in the textbook)  160分 
Work on homework problems  220分  
10.  Applications of determinants Eigenvalues and eigenvectors 
Review the content of the lecture (5.3, 6.1 in the textbook)  160分 
Work on homework problems  220分  
11.  Diagonalization Differential equations 
Review the content of the lecture (6.26.3 in the textbook)  160分 
Work on homework problems  220分  
12.  Symmetric matrices Positive definite matrices 
Review the content of the lecture (6.46.5 in the textbook)  160分 
Work on homework problems  220分  
13.  Linear transformations Choice of basis 
Review the content of the lecture (8.18.3 in the textbook)  160分 
Work on homework problems  220分  
14.  Final exam and discussions on the solutions afterwards  Preparation for the final exam  380分 
Total.      5300分 
Homework  Midterm presentation  Final exam  Total.  

1.  20%  4%  5%  29% 
2.  15%  4%  5%  24% 
3.  10%  4%  3%  17% 
4.  10%  3%  10%  23% 
5.  0%  0%  7%  7% 
Total.  55%  15%  30%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 