##### 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

#### Systems of Linear Equations

We learned that systems of linear equations can be easily solved by putting augmented matrices into reduced echelon form.

###### Worksheet - .pdf

#### Determinants and Rank

We learned that the consistency or solvability of a system is influenced by the determinant and rank of the matrix of coefficients.

###### Worksheet - .pdf

#### Singular and Invertible Matrices

We learned that if a matrix is non-singular, then it can be ``undone'' or inverted. This is handy for solving systems like Ax=b for multiple different b. We also related these notions to those of determinant, rank, and consistency of linear systems

###### Worksheet - .pdf

#### Eigenvalues and Eigenvectors

Given a system of differential equations x' = Ax, we noticed that solutions were determined by solutions to Av = (lambda)v. This introduced us to the very important notion of eigenvalue (lambda) and eigenvector (v).

###### Worksheet - .pdf