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:

- Definition of linear equation and linear system;
- What does it mean to solve a linear system?
- Representing a linear system by matrix: augmented matrix;
- How to solve a linear system? (Row Reduction Algorithm)
- Echelon form and the reduced echelon form;
- Expressing the solution of a linear system in the parametric vector form: basic/free variables
- Basic operations with vectors and their geometric interpretation:
*sum*, *scalar multiplication* - 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

- Linear combination;
- Span sets; (and geometric description when it is spanned by one or two vectors)
- Definition of matrix equation;
- Equivalence of linear system and matrix equations
- 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**

- Definition of Linear (in)dependence;
- How to verify linear (in)dependence;
- The standard matrix of a linear transformation
- Column and Null spaces
- 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

- The general definition of subspace
- Basis for a subspace
- The inverse of a matrix
- How to compute the inverse of a matrix

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