# Numerics topics

### From 6.006 Wiki

For the exam, you should:

- Be able to express a given problem as a set of linear equations and/or a set of least-squares constraints
- Be able to eliminate constraints of the form
*x*_{i}=*b*_{i}from a set of constraints. - Understand how to solve linear equations and least-squares when the coefficient matrix is upper triangular with no zeros on the diagonal.
- Understand the mechanics of a Givens rotation (which elements of
*A*and*b*are replaced by what linear combinations). - Understand how a sequence of Givens rotations can zero all the elements of a system below the main diagonal, leaving the matrix upper triangular.

You DO NOT need to be able to:

- Derive the equations for a Givens rotation.
- Understand how to treat singular problems (e.g., a triangular
*A*but with zeros on the diagonal). - Know anything about numerical stability issues