## Linear Algebra and Differential Equations - HOMEWORK

Chapter 1: Matrices and Determinants

Exercises:
1.1 Systems of Equations: 1-17 odd, 21-31 odd;
1.2 Matrices and Matrix Operations: 1-39 odd, 32;
1.3 Inverses of Matrices: 1-11 odd, 15, 19, 20, 21, 23, 25;
1.4 Special Matrices and Additional Properties of Matrices: 1-23 odd, 29-32 all;
1.5 Determinants: 1-13 odd, 15, 16, 17;
1.6 Further Properties of Determinants: 1, 3, 7, 9, 11, 15;

Chapter 2: Vector Spaces

Exercises:

2.1 Vector Spaces: 1-7 all, 9, 11;
2.2 Subspaces and Spanning Sets: 1-7 all, 9-22 all, 24, 25;
2.3 Linear Independence and Bases: 1-27 odd, 28, 30, 31;
2.4 Dimension: Nullspace, Row Space, and Column Space: 1-4 all, 5-15 odd, 16-21 all, 23-27 all;
2.5 Wronskians: 1-7 all, 11, 12, 13, 15;

Chapter 3: First Order Ordinary Differential Equations

Exercises:

3.2 Separable Differential Equations: 1-17 odd, 21;

Chapter 4: Linear Differential Equations

Exercises:

4.1 The Theory of Higher Order Linear Differential Equations: 1-11 odd;
4.2 Homogeneous Constant Coefficient Linear Differential Equations: 1-29 odd, 36, 37, 38, 43, 44, 45;

Chapter 5: Linear Transformation, Eigenvalues and Eigenvectors

Exercises:

5.1 Linear Transformations: 1-13 odd, 14, 15-27 odd, 28, 31, 32, 33, 36;
5.2 The Algebra of Linear Transformations: 1-9 odd, 11, 13, 15, 16, 17, 19, 20, 21, 22-25 all;
5.3 Matrices for Linear Tranformations: 1-11 odd, 15;
5.4 Eigenvalues and Eigenvectors of Matrices: 1-17 odd, 20-26 all;
5.5 Similar Matrices, Diagonalization, and Jordan Canonical Form: 1-31 odd, 32, 33, 34;