Properties of Dependence
- If a set of vectors is a dependent set and is a linear combination of the other vectors, then
- You can remove that vector with no change to the span
Bases
- A basis of a subspace contains just enough vectors to be the spanning set of the subspace
- A basis must be linearly independent
- A basis is the easiest way to specify which vectors are in a subspace
Chapter 3 Goals
- Understand the operations of matrix algebra and identify the similarities and differences between matrix algebra and the algebra of real numbers
- Describe, and find bases for, the row space, column space and null space of a matrix
- Find the rank and nullity of a matrix and understand how they are related by the rank-nullity theorem
- Compute determinants and understand the relationship between determinants, rank and invertibility of matrices
Review: Matrices and Determinants and the Unit Reader