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 xi = bi 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