About the first midterm exam – MATH 2130

The first midterm will be applied at September 30th. It will have two parts: first one during class and second one you will have 24h to submit your solution on Canvas.

Here is a list of topics organized by their level of “forgiveness”, importance and other criteria I don’t remember:

Unforgivable topics

You can’t conclude a linear algebra course without knowing these by heart:

1. Definition of linear equation and linear system;
2. What does it mean to solve a linear system?
3. Representing a linear system by matrix: augmented matrix;
4. How to solve a linear system? (Row Reduction Algorithm)
5. Echelon form and the reduced echelon form;
6. Expressing the solution of a linear system in the parametric vector form: basic/free variables
7. Basic operations with vectors and their geometric interpretation: sum, scalar multiplication
8. Basic operation with vectors and matrices and its geometric interpretation: multiplying a matrix by a vector

Unforgivable topics II

These are the ones you are allowed to spend a minute to remember

1. Linear combination;
2. Span sets; (and geometric description when it is spanned by one or two vectors)
3. Definition of matrix equation;
4. Equivalence of linear system and matrix equations
5. Definition of Linear transformations and examples

Very important topics

The cousins of the unforgivable topics. These are the ones that are very important now and as we progress in the course

1. Definition of Linear (in)dependence;
2. How to verify linear (in)dependence;
3. The standard matrix of a linear transformation
4. Column and Null spaces
5. How to find basis for column and null spaces

Important topics

Everything is important, but these are the ones that will be used more as we develop more abstract concepts

1. The general definition of subspace
2. Basis for a subspace
3. The inverse of a matrix
4. How to compute the inverse of a matrix