##### Winter 2014 MA212

Welcome to DE 2. To the left you'll find homework, as well as quiz and exam solutions as we take them. Below I'll be posting solutions to the daily worksheets (hopefully).

#### Matrix arithmetic

We familiarized ourselves with matrices and operations of addition, scalar multiplication, and matrix multiplication.

###### Worksheet - .pdf

#### Augmented matrices and reduced echelon form

We learned how to solve linear systems of equations by putting augmented matrices in reduced echelon form via row operations.

###### Worksheet - .pdf

#### The ``Superposition'' principle

Learned how solutions to linear homogeneous systems (so-called complimentary solutions) can be used to determine solutions to linear non-homogeneous systems. In particular, all solutions to a linear non-homogeneous system take the form of a particular solution plus the complimentary solution.

###### Worksheet - .pdf

#### Determinants and Rank

We learned about the relationship between rank and determinants.

###### Worksheet - .pdf

#### Non-singular Matrices and Their Inverses

We learned how to anticipate when a square matrix has an inverse and how to compute it.

###### Worksheet - .pdf

#### Eigenvectors and Eigenvalues

Solutions to linear systems of first order ordinary differential equations are governed by the so-called eigenvalues and eigenvectors of the associated coefficient matrix. Accordingly, we've familiarized ourselves with these terms and have gained the know-how to compute them.

###### Worksheet - .pdf