This 53 page Midterm 1 preparation guide includes examples and all theorems, lemmas, and corollaries dealing with the following topics:

**Chapter 1 Material**

- Linear Combinations
- Linear Independence and Linear Dependence
- The Null Space of a Matrix
- The Column Space of a Matrix
- Chapter Recap

**Chapter 2 Material**

- Vector Spaces and Subspaces
- Linear Independence and Spanning Sets
- Chapter Recap

**Chapter 3 Material**

- Basis and Dimension
- More on Rank and Nullity
- Chapter Recap

**Chapter 4 Material**

- One-Sides Inverses
- Chapter Recap

All problems come with** full solutions** at a cost of $30** (taxes included)**.

**Contact us to order your copy today!**

This 57 page Midterm 2 preparation guide includes examples and all theorems, lemmas, and corollaries dealing with the following topics:

**Chapter 1 Material**

- Linear Transformations of Euclidean
**n**-Space - Left Multiplication by a Matrix
- Kernel and Range
- One-to-One and Onto
- Composition of Linear Transformations

**Chapter 2 Material**

- The Matrices of a Linear Transformation
- The Matrix of
*T*Relative to*V*and*W* - Matrix Multiplication is Composition of Linear Transformations
- Matrices of the Identity
- Changing Coordinates
- Similarity of Matrices

All problems come with** full solutions** at a cost of $30** (taxes included).**

**Contact us to order your copy today!**