Subjects 
Section and Recommended Exercises 
Systems of Linear Equations 
1.1: 2 , 4, 10, 15, 18, 24, 29 
Row Reduction and Echelon Form 
1.2: 2 , 4, 8, 11, 13, 18, 20 
Vector equations 
1.3: 2 , 5, 9, 11, 13, 17, 24 
Matrix Equations 
1.4: 2 ,4,5,9, 17 
Solutions of Linear Systems 
1.5: 1 ,4,6,8,11,15, 23 
Application to Chemistry (brief) 
1.6: 7 , 9 
Linear Independence 
1.7: 1 ,4,6,7,14,16, 31 
Linear Transformations 
1.8: 2 ,4,7,9,13, 15 
Matrix form of Linear Transformations 
1.9: 5 ,7,10,15,18, 22 
Matrix Operations 
2.1: 4 ,7,9,16, 23 
Inverse of a Matrix 
2.2: 3 ,6,9,26,29, 32 
Invertible Matrices 
2.3: 2 ,6,9,11,13,14, 41 
LU Factorization 
2.5: 2 ,4,5,8,11,15, 17 
Application to Computer Graphics (brief) 
2.7: 1 ,2, 5 
Introduction to Determinants 
3.1: 3 ,8,9,12,22,24,25, 28 
Properties of Determinants 
3.2: 1 ,4,6,9,21,22,25, 26 
Cramer's Rule 
3.3: 2 ,5,8,11, 16 
Vector Spaces and Subspaces 
4.1: 8 ,24,30, 38 
Null Spaces and Columns Spaces 
4.2: 2 ,4,14,20, 24 
Linear Maps 
4.3: 4 ,5,10,14,15, 21 
Dimension of a Vector space 
4.5: 2 ,4,6,9,13,15, 18 
Rank 
4.6: 1 ,2,5,9,13,17, 18 
Application to Markov Chains (Brief) 
4.9: 2 ,4,6, 8, 10 
Exam Review 

Eigenvalues and Eigenvectors 
5.1: 3 ,7,9,13,15,17, 20 
The Characteristic Equation 
5.2: 4 ,7,9,13,15,16,20, 21 
EXAM REVIEW, COMMON MIDTERM THURSDAY,6/20/2018 

Diagonalization 
5.3: 2 ,4,6,7,8,12,17, 21 
Complex Eigenvalues 
5.5: 4 ,5,13, 14 
Inner Product, Length, and Orthogonality 
6.1: 1 ,8,10,12,14,15,16, 20 
Orthogonal Sets 
6.2: 1 ,4,8,12,16,1720, 23 
Orthogonal Projections 
6.3: 2 ,4,6,8,10,12,14, 16 
The GramSchmidt Procedure 
6.4: 1 ,4,8,9, 12 
Inner Product Spaces 
6.7: 1 ,2,4,6, 8 
Diagonalization of Symmetric Matrices 
7.1: 110,14,17,22 , 26 
Quadratic Forms 
7.2: 2 ,5,7,10,13, 21 
Exam Review 

FINAL EXAM: TUESDAY,~ JULY 17, 2018 
